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  PracticeFinal

  School: University Of California, Davis

  Course: MAT 22A

  MAT22A, Linear Algebra Final Exam March 20, 2013 1 Find eigenvalues and eigenvectors for the following matrix A =   2 1 1 0 1 2 0 0 3   (1) 1 2 2 Find the solution, u(t), to the differential equation ...

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  Practice Final

  School: University Of California, Davis

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  MAT22A, Linear Algebra Final Exam June 6, 2014 1 Find eigenvalues and eigenvectors for the following matrix A =   2 1 1 0 1 2 0 0 3  ...

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  • selftest3a

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  selftest3a

  School: Athabasca University, Athabasca

  Course: MATH 270

  ... (4 pts) 4x - by = 2 b2x - by = 3 2. Find the characteristic equation, eigenvalues, and corresponding eigenvectors for the matrix below. (4 pts) ...

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  • m345t2S11Sol

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  m345t2S11Sol

  School: Embry-Riddle Aeronautical University

  Course: MA 243

  MA 345 Differential Equations Spring 2011 Exam II Solutions Dr. E. Jacobs 1. (15 points) Let A be the following matrix: A = ( 3 1 1 3 ) a) Find all eigenvalues of A 0 = det(A - λI) = ∣∣∣ 3 - λ 1 1 3 - λ ∣∣∣∣ = 3 - λ)2 - 1 so λ1 ...

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  MAT 1341 - 2014W - Midterm 2

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  • solutions4.1-2

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  solutions4.1-2

  School: University Of British Columbia

  Course: MATH 307

  ... 1. For the following matrices find (a) all eigenvalues (b) linearly independent eigenvectors for each eigenvalue (c) the algebraic and geometric multiplicity for each eigenvalue ... two linearly independent (by inspection) eigenvectors are ...

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  solutions4.2

  School: University Of British Columbia

  Course: MATH 307

  ... has positive eigenvalues. Use the power method to find the largest and the smallest ones, and the corresponding eigenvectors. Check whether the two eigenvectors you have computed are orthogonal. ...

• 77 Pages

  • Chapter_5_Solutions

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  Chapter_5_Solutions

  School: New Jersey Institute Of Technology

  Course: MATH 337

  ... 5.1 SOLUTIONS Notes: Exercises 1–6 reinforce the definitions of eigenvalues and eigenvectors. ... 258 CHAPTER 5 • Eigenvalues and Eigenvectors ...

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  problems4.1

  School: University Of British Columbia

  Course: MATH 307

  ... 1. For the following matrices find (a) all eigenvalues (b) linearly independent eigenvectors for each eigenvalue (c) the algebraic and geometric multiplicity for each eigenvalue and state whether the matrix is diagonalizable. ...

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  Phytopharmaceutical Study of Natural Drugs

  School: Birla Institute Of Technology & Science, Pilani - Hyderabad

  Course: PHARM 101

  ... The principal components are orthogonal because they are the eigenvectors of the covariance matrix, which is symmetric. ...

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  • Finding Eigenvalues and Eigenvectors

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  Finding Eigenvalues and Eigenvectors

  School: University Of Minnesota

  Course: MATH 2373

  ... TA: Stephen McIntyre. In this lab, we learned how to find eigenvalues and eigenvectors using MatLab. Exercise 1: The Eigenvalues are 1 and 11. Eigenvectors are columns of P. A=[4 -3; -7 8] [P,D]=eig(A) P =. -0.7071 0.3939. ...

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  m345t2S11Sol

  School: Embry-Riddle Aeronautical University

  Course: MA 243

  MA 345 Differential Equations Spring 2011 Exam II Solutions Dr. E. Jacobs 1. (15 points) Let A be the following matrix: A = ( 3 1 1 3 ) a) Find all eigenvalues of A 0 = det(A - λI) = ∣∣∣ 3 - λ 1 1 3 - λ ∣∣∣∣ = 3 - λ)2 - 1 so λ1 ...

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  • 4.1 Homework Solutions

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  4.1 Homework Solutions

  School: University Of British Columbia

  Course: MATH 307

  Math 307: Problems for section 4.1–4.2 March 17, 2009 1. For the following matrices find (a) all eigenvalues (b) linearly independent eigenvectors for each eigenvalue (c) the algebraic and geometric multiplicity for each eigenvalue and state whet...

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  • M346.HW5.Solutions

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  M346.HW5.Solutions

  School: University Of Texas

  Course: M 346

  M346 (56615), Homework #5 Solutions * = graded Complex eigenvalues and eigenvectors (4.4) p. 70-71: 2. Since L((1, 0)T ) = (cos θ, sin θ)T and L((0, 1)T ) = (−sin θ, cos θ)T, the matrix of L is A = ( cos θ −sin θ sin θ cos θ ) . The ei...

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  • quiz12sol

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  quiz12sol

  School: University Of Texas, Arlington

  Course: MATH 3330

  MATH 3330-001 Matrices and Linear Algebra Solutions to Quiz 12 Problem 1. (10pts) Find the eigenvalues and eigenvectors of the following matrices. What are the algebraic and geometric multiplicities of these eigenvalues? A = ⎡ ⎣ 3 1 1 0 3 1 0 ...

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  • PracticeFinal

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  PracticeFinal

  School: University Of California, Davis

  Course: MAT 22A

  MAT22A, Linear Algebra Final Exam March 20, 2013 1 Find eigenvalues and eigenvectors for the following matrix A =   2 1 1 0 1 2 0 0 3   (1) 1 2 2 Find the solution, u(t), to the differential equation ...

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  • Practice Final

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  Practice Final

  School: University Of California, Davis

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  MAT22A, Linear Algebra Final Exam June 6, 2014 1 Find eigenvalues and eigenvectors for the following matrix A =   2 1 1 0 1 2 0 0 3  ...

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  • selftest3a

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  selftest3a

  School: Athabasca University, Athabasca

  Course: MATH 270

  ... (4 pts) 4x - by = 2 b2x - by = 3 2. Find the characteristic equation, eigenvalues, and corresponding eigenvectors for the matrix below. (4 pts) ...

• 12 Pages

  • Sample Final

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  Sample Final

  School: University Of California, Irvine

  Course: MATH Math 4

  ... Find the eigenvalues and corresponding eigenvectors for A. Find the orthogonal ... 11 Find the eigenvalues and eigenvectors of A. A =  ...

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  • MAT 1341 - 2014W - Midterm 2

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  MAT 1341 - 2014W - Midterm 2

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Eigenvectors Homework Help

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  • solutions4.1-2

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  solutions4.1-2

  School: University Of British Columbia

  Course: MATH 307

  ... 1. For the following matrices find (a) all eigenvalues (b) linearly independent eigenvectors for each eigenvalue (c) the algebraic and geometric multiplicity for each eigenvalue ... two linearly independent (by inspection) eigenvectors are ...

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  solutions4.2

  School: University Of British Columbia

  Course: MATH 307

  ... has positive eigenvalues. Use the power method to find the largest and the smallest ones, and the corresponding eigenvectors. Check whether the two eigenvectors you have computed are orthogonal. ...

• 77 Pages

  • Chapter_5_Solutions

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  Chapter_5_Solutions

  School: New Jersey Institute Of Technology

  Course: MATH 337

  ... 5.1 SOLUTIONS Notes: Exercises 1–6 reinforce the definitions of eigenvalues and eigenvectors. ... 258 CHAPTER 5 • Eigenvalues and Eigenvectors ...

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  problems4.1

  School: University Of British Columbia

  Course: MATH 307

  ... 1. For the following matrices find (a) all eigenvalues (b) linearly independent eigenvectors for each eigenvalue (c) the algebraic and geometric multiplicity for each eigenvalue and state whether the matrix is diagonalizable. ...

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  School: University Of Washington

  Course: MATH 308

  Math 308 Solutions Sec. 3.1 Problems(1,3,7,15,17,19) page 1 3.1.1 Find the eigenvalues and eigenvectors for A =    1 ... a) So λ = 1 and λ = 3 are eigenvalues. b) Eigenvectors associated with λ = 1 are in N(A − I): A − I =   ...

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  MATH 225 Homework 6 Solutions

  School: University Of Alberta

  Course: MATH 225

  Math 225 (A1) Solution to Homework Assignment 6 1. Using the eigenvalues and their corresponding eigenvectors of A, the matrix A can ... 4 0 1 −2 1 0 −2 0 1 ⎞ ⎠. Using eigenvalues and their corresponding eigenvectors, ...

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  • HW10_Sol

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  HW10_Sol

  School: New York University

  Course: MATHEMATIC MATH UA 12

  ... 2. Follow those eigenvectors by e0t x1 and e 5t x2 3. The solution ut/ D x1 C e 5t x2 has steady state x1 D .3; 2/. ... 5 QD 1 3 " 2 1 2 2 2 1 1 2 2# . The columns of Q are unit eigenvectors of A Each unit eigenvector could be multiplied ...

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  • HW14-solutions

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  HW14-solutions

  School: University Of Texas

  Course: M 340L

  ... When u1 = [ 2 −1 ], u2 = [ 1 2 ] , are eigenvectors of a symmetric 2 × 2 matrix A corresponding to eigenvalues ... Now set v1 = u1 ∥u1∥ , v2 = u2 ∥u2∥ , v3 = u3 ∥u3∥ , where u1, u2, u3 are eigenvectors of A corre- sponding to λ...

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  • HW15-solutions

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  HW15-solutions

  School: University Of Texas

  Course: M 340L

  ... (λ - 16)(λ - 1) = 0 , ie, λ1 = 16, λ2 = 1. Eigenvectors x1 and x2 associated with λ1 and λ2 are x1 = [ 1 2] , x2 = [ -2 1 ] ; these are orthogonal. The associated or- thonormal eigenvectors are thus v1 = 1 /5 [ 1 2] , v2 = 1 /5 [ -2 1 ] ...

• 10 Pages

  • HW11-solutions

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  HW11-solutions

  School: University Of Texas

  Course: M 340L

  ... 010 10.0 points Let A be a 2 × 2 matrix with eigenvalues 2 and −1 and corresponding eigenvectors v1 = [ 3 3 ] , v2 = [ −2 −1 ] . ... 4 shows that x0 = −3v1 +3v2. Since v1 and v2 are eigenvectors (for the eigenvalues 2 and −1 respect...

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  • HW10-solutions

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  HW10-solutions

  School: University Of Texas

  Course: M 340L

  ... x2 x1 are eigenvectors corresponding to eigenvalues λ1 = −3 and λ2 = 1 respectively for a 2 × 2 matrix A. ... 1. FALSE correct 2. TRUE Explanation: If two eigenvectors correspond to distinct eigenvalues then they are linearly indepen- den...

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  • Exercise_solutions_chapter3

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  School: Auckland

  Course: MATHS 108

  ... But it is easy to find eigenvectors. Let f (x) = a0 + a1 x + . . . + an xn with a. ... 1. Since the space is infinitely-dimensional we cannot find eigenvalues using the characteristic polynomial. But it is easy to find eigenvectors. Let f(x) =...

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  • 2050-assignment9

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  2050-assignment9

  School: Memorial University Of Newfoundland

  Course: MATH 2050

  ... Fall 2015 Do not need to hand in Note that the final exam also covers material after HW8, including, for instance, calculating determinant by row operations, eigenvalues and eigenvectors, similarity and diagonalization etc. ...

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  • warmup19

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  warmup19

  School: Georgia Institute Of Technology

  Course: MATH 1502

  ... (a) A matrix A is not invertible if 0 is an eigenvalue of A. (b) If v1 and v2 are linearly independent eigenvectors of A, then they must correspond to different eigenvalues. ... (d) The eigenvectors are in the range of the matrix A − λI. ...

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  • hw1

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  hw1

  School: University Of Utah

  Course: MATH 3150

  ... (1) (4.6.24) Given mutually orthogonal vectors v1,v2,...,vk in Rk show that |v1 + v2 + ··· + vk|2 = |v1|2 + |v2|2 + ··· + vk|2 (2) (6.1.20) Determine the eigenvalues and eigenvectors of the matrix   1 0 0 −4 7 2 10 −15 −4 ...

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  • Linear Algebra- Tutorial 2

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  Linear Algebra- Tutorial 2

  School: McGill University

  Course: MATH 270

  Math 270, Tutorial 2: Eigenvalues & Eigenvectors Math 270, tutorial 2 ... What are the eigenvectors and eigenvalues of a matrix? The eigenvectors of a matrix are the vectors whose direction ...

Eigenvectors Lab Reports

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  • Phytopharmaceutical Study of Natural Drugs

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  Phytopharmaceutical Study of Natural Drugs

  School: Birla Institute Of Technology & Science, Pilani - Hyderabad

  Course: PHARM 101

  ... The principal components are orthogonal because they are the eigenvectors of the covariance matrix, which is symmetric. ...

• 4 Pages

  • Finding Eigenvalues and Eigenvectors

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  Finding Eigenvalues and Eigenvectors

  School: University Of Minnesota

  Course: MATH 2373

  ... TA: Stephen McIntyre. In this lab, we learned how to find eigenvalues and eigenvectors using MatLab. Exercise 1: The Eigenvalues are 1 and 11. Eigenvectors are columns of P. A=[4 -3; -7 8] [P,D]=eig(A) P =. -0.7071 0.3939. ...

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  School: Rutgers University

  Course: MATH 550

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  School: San Jose State University

  Course: MATH 129a

Eigenvectors Notes

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  • m345t2S11Sol

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  m345t2S11Sol

  School: Embry-Riddle Aeronautical University

  Course: MA 243

  MA 345 Differential Equations Spring 2011 Exam II Solutions Dr. E. Jacobs 1. (15 points) Let A be the following matrix: A = ( 3 1 1 3 ) a) Find all eigenvalues of A 0 = det(A - λI) = ∣∣∣ 3 - λ 1 1 3 - λ ∣∣∣∣ = 3 - λ)2 - 1 so λ1 ...

• 8 Pages

  • 4.1 Homework Solutions

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  4.1 Homework Solutions

  School: University Of British Columbia

  Course: MATH 307

  Math 307: Problems for section 4.1–4.2 March 17, 2009 1. For the following matrices find (a) all eigenvalues (b) linearly independent eigenvectors for each eigenvalue (c) the algebraic and geometric multiplicity for each eigenvalue and state whet...

• 2 Pages

  • M346.HW5.Solutions

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  M346.HW5.Solutions

  School: University Of Texas

  Course: M 346

  M346 (56615), Homework #5 Solutions * = graded Complex eigenvalues and eigenvectors (4.4) p. 70-71: 2. Since L((1, 0)T ) = (cos θ, sin θ)T and L((0, 1)T ) = (−sin θ, cos θ)T, the matrix of L is A = ( cos θ −sin θ sin θ cos θ ) . The ei...

• 3 Pages

  • quiz12sol

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  quiz12sol

  School: University Of Texas, Arlington

  Course: MATH 3330

  MATH 3330-001 Matrices and Linear Algebra Solutions to Quiz 12 Problem 1. (10pts) Find the eigenvalues and eigenvectors of the following matrices. What are the algebraic and geometric multiplicities of these eigenvalues? A = ⎡ ⎣ 3 1 1 0 3 1 0 ...

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  • math471_hw5

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  math471_hw5

  School: University Of Michigan

  Course: MATH 471

  Math 471 Fall 2009 Homework 5 due: Fri Nov 13 1. Find the eigenvalues and eigenvectors of the following matrices. Do this by hand, but you may check your answers using Matlab. a) ( 2 0 0 1) b) ( 0 2 1 0) c) ( 2 −1 −1 2) d)    2 −1 0...

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  • lab12.desc

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  lab12.desc

  School: Purdue University

  Course: MA 366

  LAB #12 Linearization Goal: Investigate the local behavior of a nonlinear system of differential equations near its equilibrium points by linearizing the system. Required tools: Matlab routine pplane ; eigenvalues and eigenvectors. Discussion In t...

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  • Math 240

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  Math 240

  School: University Of Pennsylvania

  Course: MATH 240

  ... [15 problems, 7 multiple choice]. 1) (d). 2) a) rank=3. b) det =0. c) 1. 3) (b). 4) only 2 eigenvectors. 5) (a). 6) x_1=c1*t*exp(2t) +c2*exp(2t). 7) (c). 8) y= (2cos(2t)+2sin(2t) ) exp(-t). 9) y=3x-1/x. 10) a_{n+2}=- (n-1)/(n+2) a_n , y=1+2x+x...

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  • 4.2

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  4.2

  School: Virginia Tech

  Course: MATH 1114

  4.2 Applications of Eigenvalues/Eigenvectors – Markov Chains. A Markov chain is a discrete-time stochastic process used to model certain systems in physics and statistics, for example. With a Markov Chain, a transition matrix is used to predict f...

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  • Hw1080_3sols

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  Hw1080_3sols

  School: University Of Pittsburgh

  Course: MATH 1080

  Math 1080: Spring 2005 Homework #3 Problem 1: Show that the Householder reflector T 2ww IH - = , with 1 = w , is symmetric and orthogonal. Find the eigenvalues and eigenvectors of H. SOLUTION: Symmetry: ( ) ( ) H ww I ww I ww I H = - = - = T TT TT...

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  • Exam 3 sol

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  Exam 3 sol

  School: University Of Maryland

  Course: MATH 246

  Third In-Class Exam Solutions Math 246, Professor David Levermore Thursday, 29 November 2012 (1) [6] Given that 2 is an eigenvalue of the matrix A =   2 2 −1 1 1 0 3 −1 1   , find all the eigenvectors of A assoc...

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  • hw10solutions

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  hw10solutions

  School: Haverford College

  Course: MATH 215

  Math 215 HW #10 Solutions 1. Problem 5.2.14. Suppose the eigenvector matrix S has ST = S−1. Show that A = SΛS−1 is symmetric and has orthogonal eigenvectors. Proof. Suppose S = [ v1 ... vn], where vi are the eigenvectors of A. Then, since ST ...

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  • Lab 5

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  Lab 5

  School: Rutgers University

  Course: MATH 250C

  Math 250-C Matlab Assignment #5 1 Revised 12/06/12 LAB 5: Eigenvalues and Eigenvectors In this lab you will use Matlab to study these topics: • The geometric meaning of eigenvalues and eigenvectors of a matrix • Determination of eigenvalues and ...

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  • HWsolutions13

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  HWsolutions13

  School: University Of California, Berkeley

  Course: MATH 110

  HOMEWORK 13 SOLUTIONS Problem (§7.1 # 1). Label the following statements as true or false. Proof. (a) Eigenvectors of a linear operator T are also generalized eigenvectors of T. True. By Theorem 7.1.a, Kλ ⊇ Eλ. (b) It is possible for a genera...

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  • 6_1_Eigenvalues_and_eigenvectors

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  6_1_Eigenvalues_and_eigenvectors

  School: University Of New South Wales

  Course: MATH 2019

  6.1 EIGENVALUES AND EIGENVECTORS Given a square matrix A, a non-zero vector v is said to be an eigenvector of A if Av = v for some R. The number is referred to as the eigenvalue of A associated with v. We first find eigenvalues by ...

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  • 6_4_Systems_of_ODEs

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  6_4_Systems_of_ODEs

  School: University Of New South Wales

  Course: MATH 2019

  ... Ay. The system is easily solved by finding the eigenvalues and eigenvectors of A. If A is a 3 3 matrix with. ... y = Ay. The system is easily solved by finding the eigenvalues and eigenvectors of A. If ...

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  • pictures of eigenvectors

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  pictures of eigenvectors

  School: McMaster University

  Course: MATH 1b03

  0 A=/§,f}| has eiopwalnes and eigenvectors x , , * , = f¥ ; xz=2 , *,=f÷f : a }=} , * fi , ] Axz = 2*2 )A*i=* ' Def # Ki t $3← Xz By ×*×¥ )pµ=*} * / 5 - 1 1 09 A=fz4 ;, z , ) has eiopwalnes and eigenvectors a=4 , * ' =/ xz=x} ...

Eigenvectors Test Prep

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  • PracticeFinal

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  PracticeFinal

  School: University Of California, Davis

  Course: MAT 22A

  MAT22A, Linear Algebra Final Exam March 20, 2013 1 Find eigenvalues and eigenvectors for the following matrix A =   2 1 1 0 1 2 0 0 3   (1) 1 2 2 Find the solution, u(t), to the differential equation ...

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  • Practice Final

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  Practice Final

  School: University Of California, Davis

  Course: MAT 22A

  MAT22A, Linear Algebra Final Exam June 6, 2014 1 Find eigenvalues and eigenvectors for the following matrix A =   2 1 1 0 1 2 0 0 3  ...

• 2 Pages

  • selftest3a

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  selftest3a

  School: Athabasca University, Athabasca

  Course: MATH 270

  ... (4 pts) 4x - by = 2 b2x - by = 3 2. Find the characteristic equation, eigenvalues, and corresponding eigenvectors for the matrix below. (4 pts) ...

• 12 Pages

  • Sample Final

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  Sample Final

  School: University Of California, Irvine

  Course: MATH Math 4

  ... Find the eigenvalues and corresponding eigenvectors for A. Find the orthogonal ... 11 Find the eigenvalues and eigenvectors of A. A =  ...

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  • Math 194_Study Guide on the Invertible Matrix Theorem - Eigenvalues and Eigenvectors

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  Math 194_Study Guide on the Invertible Matrix Theorem - Eigenvalues and Eigenvectors

  School: Vanderbilt University

  Course: MATH 194

  Math 194 The Invertible Matrix Theorem (Unit 5 Version) Let A be a square n × n matrix. Then the following statements are equivalent. That is, for a given A, the statements are either all true or all false. 1. A is an invertible matrix. ...

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  • SampleFinal

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  SampleFinal

  School: University Of California, Irvine

  Course: MATH 44370

  Math 4 Sample Final 1. 2 1 A=4 0 1 0 2 0 3 1 0 5 1 Find the eigenvalues and corresponding eigenvectors for A. Find the orthogonal matrix Q that is used to diagonalize A. 1 2. A= 1 2 2 1 Compute: A 1 eigenvalues of A eigenvalues of A 1 ...

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  • Quiz 9 Solution on Differential Equations and Linear Algebra

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  Quiz 9 Solution on Differential Equations and Linear Algebra

  School: University Of Utah

  Course: MATH 2250

  Math 2250 Quiz 9 July 25, 2014 Name 1. [5 pts.] Compute the eigenvalues and eigenvectors of the following matrix. A = [10 −9 6 −5 ] Solution: ∣ ∣ ∣ ∣ 10 − λ −9 6 −5 − λ ∣ ∣ ∣ ∣ = λ − 10)(λ + 5) + 54 = λ2 − 5λ ...

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  • Sample+Final

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  Sample+Final

  School: University Of California, Irvine

  Course: MATH 4

  ... 1 0 −1 0 −2 0 −1 0 1   Find the eigenvalues and corresponding eigenvectors for A. Find the orthogonal matrix Q that is used to diagonalize A. 1 ... 11 15. A = [ 2 0 0 3 ] Find the eigenvalues and eigenvectors of A. A =   ...

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  • Sample+Midterm+1

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  Sample+Midterm+1

  School: University Of California, Irvine

  Course: MATH 4

  Math 4 Sample Midterm 1. A = 1 2 2 4 Find the eigenvalues and corresponding eigenvectors for A. Find the orthogonal matrix Q that is used to diagonalize A. 1 2. A =  3 1 1 1 -1 1 1 0 1   Calculate: trace(A) |A| ...

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  • EXAM04-solutions

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  EXAM04-solutions

  School: University Of Texas

  Course: M 340L

  ... (λ − 16)(λ − 1) = 0 , ie, λ1 = 16, λ2 = 1. Eigenvectors x1 and x2 associated with λ1 and λ2 are x1 = [ 2 1] , x2 = [ −1 2 ] ; these are orthogonal. Associated orthonormal eigenvectors are thus v1 = 1 √5 [ 2 1] , v2 = 1 √5 [ −...

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  • EXAM03-solutions

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  EXAM03-solutions

  School: University Of Texas

  Course: M 340L

  ... Explanation: Since v1 and v2 are eigenvectors corre- sponding to distinct eigenvalues of A, they form an eigenbasis for R2. Thus ... 004 10.0 points If eigenvectors of an n × n matrix A are a basis for Rn, then A is diagonalizable. ...

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  • tut_no6

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  tut_no6

  School: IIT Bombay

  Course: MA 106

  MA 106 Linear Algebra (Spring 2016) Tut Sheet 6: Eigenvalues and Eigenvectors 1. If the n × n matrices A and ˜A are similar (ie ˜A = P−1AP for some nonsingular n × n matrix P) then ...

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  • quiz9-solution

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  quiz9-solution

  School: University Of Illinois, Chicago

  Course: MATH 310

  QUIZ 9 Math 310 Name: Problem 1. Consider the matrix A = [ 5 4 -2 -1 ] . a) (3pt) Find the characteristic polynomial χA(λ) of A. b) (2pt) Find all eigenvalues of A. (No need to find eigenvectors) Solution. ...

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  • sample_midterm2

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  sample_midterm2

  School: Stony Brook University

  Course: AMS 210

  ... 1) (20 points) Given ⎥ ⎦ ⎤ 32 12 ~ A a) (10 pts.) Determine the eigenvalues of the matrix. b) (10 pts.) Determine the eigenvectors of the matrix. 2) (35 points) Given ⎥ ⎥ ⎥ 4 2 2 ...

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  • math339midreview

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  math339midreview

  School: Clarkson University

  Course: MA 339

  ... A = ⎡ ⎣ 1 0 0 0 1 1 0 1 1 ⎤ ⎦. (a) Find the eigenvalues and eigenvectors. (b) Diagonalize A, that is, find matrices P and D such that A = PDP−1. (c) Compute A7 using the decomposition in part b. (2) (a) Find the LU decomposition A = ...

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  • PS6_Soln+

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  PS6_Soln+

  School: IIT Kanpur

  Course: MTH 102

  ... Problems marked (T) are for discussions in Tutorial sessions. 1. Find the eigenvalues and corresponding eigenvectors of matrices (a) [ 1 1 4 1 ] (b)   ... 2. Construct a basis of R3 consisting of eigenvectors of the following matrices (a...