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Georgia Tech | MATH 1522
Linear Algebra For Calc
Professors
• Allen K. Hoffmeyer,
• Saikat Biswas,
• ,
• Hein Van Der Holst,
• Mccuan,
• Geronimo

#### 62 sample documents related to MATH 1522

• Georgia Tech MATH 1522
Math 1522, Exam 1: 1.1-5, 1.7-9 Name/Date: 1. (25 points) (1.2.14) Find every x1 , x2 , x3 , x4 , and x5 such that 3 8 0 5 0 1 0 6 1 4 1 0 x1 + x2 + x3 0 0 + x4 0 + x5 1 = 0 0 0 0 0 0 0 0 Solution: We form a matrix with the given vectors in the colu

• Georgia Tech MATH 1522
Math 1522, Quiz 2: 1.5-9 (practice) Name/Section: 1. (50 points) (1.7.5) Is the collection of vectors linearly dependent or linearly independent? 9 3 0 2 1 7 , , 1 4 5 2 4 1 Solution: The matrix with these vectors as columns and its reduction are as fo

• Georgia Tech MATH 1522
Math 1522, Exam 1: 1.1-5, 1.7-9 (practice) Name/Section: 1. (25 points) (1.2.13) Find the general solution of the system whose augmented matrix is 1 3 0 1 0 2 0 10 0 4 1 0 00 1 9 4 0 00 0 0 0 Solution: This system is already in echelon form with and fourt

• Georgia Tech MATH 1522
Math 1522, Quiz 1: 1.1-5 (practice) Name/Section: 1. (50 points) (1.1.13) Solve the system by Gaussian elimination. x1 3x3 = 8 2x1 +2x2 +9x3 = 7 x2 +5x3 = 2 Solution: The augmented matrix associated with this system and its reduction are as follows: 1 0 3

• Georgia Tech MATH 1522
Math 1522, Quiz 2: 1.5-9 (practice) Name/Section: 1. (50 points) (1.7.1) Is the collection of vectors linearly dependent or linearly independent? 7 9 5 0 , 2 , 4 0 6 8 Solution: The matrix with these vectors as columns and its reduction are as follows

• Georgia Tech MATH 1522
Math 1522, Exam 2: 2.1-3,5,8-9, 3.1-3, 4.1-3 1. (25 points) (2.3.20,21) If A is a 3 3 matrix and 1 4 2 = A 5 , A 3 6 then nd 10 A 10 . 10 Solution: Notice that 0 4 1 3 0 = A 5 A 2 = A 3 0 6 3 3 Therefore, 3 0 10 10 = 10 A 3 = 0 . A 3 3 0 10 2. (25 poi

• Georgia Tech MATH 1522
Math 1522, Quiz 3: 2.1-3 Name/Section: 1. (50 points) (2.1.2) Let A= 35 1 4 and B= 7 5 1 1 4 3 . Find AB . Solution: AB = 35 1 4 7 5 1 1 4 3 = 26 35 12 3 11 13 . 2. (50 points) (2.2.31) Find the inverse of the matrix 1 0 2 3 1 4 . 2 3 4 Solution: We appe

• Georgia Tech MATH 1522
Math 1522, Quiz 4: 2.8-3.2 (practice) Name/Section: 1. (50 points) (2.8.9) Let 2 3 4 8 6 . A = 8 6 7 7 Is 6 v = 10 11 in the null space of A? Solution: Remember that the null space of A is cfw_x : Ax = 0. Thus, we simply need to calculate Av and see if i

• Georgia Tech MATH 1522
Math 1522, Exam 2: 2.1-3,5,8-9, 3.1-3, 4.1-3 (practice) 1. (25 points) (2.3.20,21) If A is a 3 3 matrix and 2 1 A 1 = A 0 , 7 0 then show the equation Ax = 0 has more than one solution. Solution: Notice that x = 0 (the zero vector) is would be 2 1 1 0 =

• Georgia Tech MATH 1522
Math 1522, Quiz 3: 2.1-5 (practice) Name/Section: 1. (50 points) (2.1.9) Let A= 23 1 1 19 3 k and . Find all values of k such that AB = BA. Solution: The product matrices are AB = 7 18 + 3k 4 9 + k and BA = 7 12 6 k 9 + k . In order for these to be the sa

• Georgia Tech MATH 1522
Math 1522, Quiz 4: 2.8-3.2 (practice) Name/Section: 1. (50 points) (2.8.10) Let 2 2 0 3 5 , A= 0 6 3 5 and let L be the linear transformation determined by L(x) = Ax. Is 5 v= 5 3 in the kernel of L? Solution: Remember that the kernel is cfw_x : L(x) = 0.

• Georgia Tech MATH 1522
Math 1522, Quiz 5: 4.4-7 (practice) Name/Section: 1. (50 points) (4.4.5) If the vector 1 1 x= , is expressed in the basis 1 2 , 3 5 , what are its new coordinates? Solution: The new coordinates are c1 c2 where 1 1 = c1 1 2 3 5 + c2 . These values may be f

• Georgia Tech MATH 1522
Math 1522, Quiz 6: 5.1-5 (practice) Name/Section: 1. (50 points) (5.1.7) Find an eigenvector of the matrix 3 0 1 1 A= 2 3 3 4 5 corresponding to the eigenvalue 4. Solution: We are looking for a nonzero solution of the homogeneous ciated with A 4I : 1 0 1

• Georgia Tech MATH 1522
Math 1522 Final Exam: Ch. 1-5 (practice) 1. (25 points) (5.3.1) If A 20 01 and 57 23 , 3 7 2 5 . P= Compute P AP 1. Solution: First we must compute the inverse of P : P 1 = 1 (P )cof )T = det(P ) Then we just multiply: P AP 1 = 57 23 20 01 3 7 2 5 = 10 7

• Georgia Tech MATH 1522
Math 1522 Practice Final Exam 1a. Find the eigenvalues and corresponding eigenvectors to the matrix A= 1 4 -2 -8 Fall 07 b. Find A15 (Show all work). c. Let A be an nn matrix. Show that eigenvectors associated with different eigenvalues of A are linearly

• Georgia Tech MATH 1522
Math 1522 Practice Test 1 Fall 07 1. Consider the matrices A= 1 1 2 1 1 1 1 1 B= 2 1 3 0 1 3 2 1 (a) Find 3A + 2B (b) Find 2AT + 3B T 2. Let 1 1 A= 1 1 1 1 2 1 2 1 = 7 b 1 1 1 3 (a) Row reduce A to row echolon form. (b) Find the pivotal columns of A, Lis

• Georgia Tech MATH 1522
Math 1522 1. Consider Practice Test 2 2 A = 1 0 0 1 1 1 1. 2 Geronimo (a) If it exists find A-1 (b) Write out the elementary matrices you used to perform the first three elementary row operations in the above calculation. 2. Determine between which spaces

• Georgia Tech MATH 1522
Math 1522 Practice Test 3 Geronimo 1. Find the range and null space of the following matrices. spaces. 1122 1 2 3 1 5 1 (a) A = (b) A = 1213 1 Find a basis for each of these 2 1 1 3 1 1 2. Compute the determinant of the following matrices (a) 2101 1 2 1

• Georgia Tech MATH 1522
Math 1522 Practice Test 5 Geronimo 1.a Find the best linear t to the points (xi , yi ) i = 1.3 given by, (1, 2) (2, 3), (3, 2) 1.b Suppose that C is an m m matrix with linearly independent columns. Show that C T C is inverible. 3 2.a Let u = 1 and W is th

• Georgia Tech MATH 1522
Math 1522 H Instructor: Syllabus Fall 2008 Ian Palmer - Skiles 147 - icpalm@math.gatech.edu Oce Hours: MF after class or by appointment Lecture: MWF 11-12 - IC 213 www.math.gatech.edu/icpalm Elementary Linear Algebra Spence, Insel, and Friedberg (

• Georgia Tech MATH 1522
MATH 1522 - SECTION M - FALL 2008 SYLLABUS Math 1522 Introduction to Linear Algebra for Calculus MW 15:05-16:25 D.M. Smith Bldg 105 Ulfar F. Stefnsson a Oce: Skiles 166 Oce Phone: (404)-894-5256 Email Address: ulfar@gatech.edu Oce Hours: MW 10-11 an

• Georgia Tech MATH 1522
MATH 1522 C QUIZ #1 NAME: September 2, 2005 Answer the following questions clearly and completely. 121 241 x1 1 1 x . , x = 2 , and b = x3 1 0 x4 |1 . Clearly show your steps in the row-reduction process. |1 1. Let A = (6 points) a. Find the

• Georgia Tech MATH 1522
MATH 1522 TERMINOLOGY REVIEW SHEET Fall 2005 C. Heil Below is a quick list of some of the terminology and other highlights from the sections of the text that we will covere. You should be understand each item and be able to use or dene it as appro

• Georgia Tech MATH 1522
MATH 1522 When and Where FINAL EXAM: INSTRUCTIONS December 15, 2005 The exam is scheduled for 8:0010:50 a.m. on Thursday, December 15. Please arrive by 7:55. The exam will take place in our regular classroom, Skiles 146. What to Bring (and Not

• Georgia Tech MATH 1522
MATH 1522 When and Where FINAL EXAM: INSTRUCTIONS May 5, 2005 The exam starts sharply at 8:00 a.m. on Thursday, May 5. Please arrive by 7:55. The exam will take place in our regular classroom, Skiles 146. What to Bring (and Not to Bring) Calc

• Georgia Tech MATH 1522
MATH 1522 Section M Due in class on September 17th 2008 Homework Assignment 1 Name: gtID #: Note: There are 11 problems in this assignment, and eight of them will be graded. Write out your solutions neatly and explain your work. Use extra sheets

• Georgia Tech MATH 1522
MATH 1522 SELECTED CHAPTER #5 SOLUTIONS Fall 2005 5.1 #1a. False. v must be nonzero. c. True. If there\'s a nonzero x such that (A - In )x = 0, then Ax - x = 0, so Ax = x. e. True. Any nonzero multiple of an eigenvector is another eigenvector. In f

• Georgia Tech MATH 1522
MATH 1522 QUIZ 1 QUIZZES AND EXAMS FALL 2001 (2 points) 1. Complete the following: a linear combination of vectors u1 , u2 , . . . , un in Rm is (2 points) 2. Suppose that A is an m n matrix and the columns of A are the vectors x1 . . How do

• Georgia Tech MATH 1522
MATH 1522 Section M October 27, 2008 PRACTICE EXAM 2 Name: gtID#: Note: The exam is worth 100 points and there are ve problems. Write out your solutions neatly and explain your work. The use of calculators is not allowed. Problem 1 (20 points). De

• Georgia Tech MATH 1522

• Georgia Tech MATH 1522
MATH 1522 C QUIZ #5 NAME: December 2, 2005 Answer the following questions clearly and completely. 1 5 1. Let u1 = 1 and u2 = 1 . Let V = span{u1 , u2 }. 1 2 (8 points) a. Use the Gram-Schmidt procedure to nd an orthogonal basis for V . (Pr

• Georgia Tech MATH 1522
MATH 1522 C QUIZ #3 NAME: October 21, 2005 Answer the following questions clearly and completely. 2 0 1. Let A = 3 1 1 2 1 1 2 0 1 3 3 0 . 2 0 (6 points) a. Compute det(A) by using cofactors to reduce the 4 4 determinant to a sum of 3 3 dete

• Georgia Tech MATH 1522
MATH 1522 C QUIZ #2 NAME: October 21, 2005 Answer the following questions clearly and completely. (9 points) 1. Let A = 1 2 0 0 3 1 , B= , x= . 1 2 1 1 1 2 Either compute the following products or write Undened if not dened. a. AB = b. xT A = c.

• Georgia Tech MATH 1522
MATH 1522 C When and Where QUIZ #3: INSTRUCTIONS October 21, 2005 The quiz will take place in the last 20 minutes of class on Friday, October 21, 2005. The quiz will take place in our regular classroom, Skiles 146. What to Bring (and Not to Br

• Georgia Tech MATH 1522
MATH 1522 FINAL EXAM NAME: SOLUTIONS May 5, 2005 Answer the following questions clearly and completely. Unless otherwise specied, you must provide work justifying your solution. There are 6 questions plus one extra credit problem, on 12 pages. The

• Georgia Tech MATH 1522

• Georgia Tech MATH 1522
MATH 1522 Section M Due in class on October 27, 2008 Homework Assignment 2 Name: Note: gtID #: There are 12 problems in this assignment, and six of them will be graded (you still need to do all the problems, the six graded problems are xed). Writ

• Georgia Tech MATH 1522
MATH 1522 Section M October 27, 2008 PRACTICE EXAM 2 Name: gtID#: Note: The exam is worth 100 points and there are ve problems. Write out your solutions neatly and explain your work. The use of calculators is not allowed. Problem 1 (20 points). De

• Georgia Tech MATH 1522
MATH 1522 Section M September 22, 2008 PRACTICE EXAM 1 Name: gtID#: Note: The exam is worth 100 points and there are ve problems. Write out your solutions neatly and explain your work. The use of calculators is not allowed. Problem 1 (14 points) (

• Georgia Tech MATH 1522
MATH 1522 SYLLABUS FALL 2005 Course Number: Math 1522 C Course Name: Lecture Time: Lecture Room: Instructor: Linear Algebra for Calculus MWF 10:0510:55 a.m. Skiles 146 Dr. Christopher Heil Office: Skiles 260 Office Phone: (404) 894-9231 Email Addres

• Georgia Tech MATH 1522
MATH 1522 EXAM #2 NAME: March 14, 2005 Answer the following questions clearly and completely. Unless otherwise specied, you must provide work justifying your solution. There are 5 questions plus one extra credit problem, on 8 pages. The exam is wo

• Georgia Tech MATH 1522
MATH 1522 EXAM #1 NAME: February 11, 2005 Answer the following questions clearly and completely. Unless otherwise specied, you must provide work justifying your solution. There are 5 questions plus one extra credit problem, on 7 pages. The exam is

• Georgia Tech MATH 1522
MATH 1522 SELECTED CHAPTER #1 SOLUTIONS Fall 2005 1.1 #39. We\'re told that B is a square matrix, and we\'re asked to show that B + B T is symmetric. One way is to write out the entries of B, and then compute B T and add it to B. Another, simpler, w

• Georgia Tech MATH 1522
MATH 1522 HOMEWORK #4: INSTRUCTIONS DUE: April 18, 2005 Work the problems listed on the second page. This homework is worth 20 points total, with 10 of these points being bonus points. Note the following rules: You will lose points if you do not f

• Georgia Tech MATH 1522
MATH 1522 FINAL EXAM NAME: December 15, 2005 Answer the following questions clearly and completely. Unless otherwise specified, you must provide work justifying your solution. There are 8 questions plus two extra credit problems, on 13 pages. The

• Georgia Tech MATH 1522
MATH 1522 4.1 #8. Since SELECTED CHAPTER #4 SOLUTIONS Fall 2005 r - s + 3t 1 -1 3 2r - t 2 0 -1 = r + s + t , -r + 3s + 2t -1 3 2 -2r + s + t -2 1 1 we see that 1 -1 3 r - s + 3t 2r - t 2 0 -1 S = : r,

• Georgia Tech MATH 1522
MATH 1522 C EXAM #1 NAME: September 9, 2005 Answer the following questions clearly and completely. Unless otherwise specied, you must provide work justifying your solution. There are 5 questions plus one extra credit problem, on 6 pages. The exam

• Georgia Tech MATH 1522
MATH 1522 Section M Due in class on September 17th 2008 Homework Assignment 1 Name: gtID #: Note: There are 11 problems in this assignment, and eight of them will be graded. Write out your solutions neatly and explain your work. Use extra sheets

• Georgia Tech MATH 1522
MATH 1522 C EXAM #3 NAME: November 11, 2005 Prove that W is a subspace of R3 . You may use any valid method to prove this, but be sure to give a clear and careful proof. Answer the following questions clearly and completely. Unless otherwise spec

• Georgia Tech MATH 1522
MATH 1522 3.1 #13. 1 2 2 1 0 1 2 3 1 SELECTED CHAPTER #3 SOLUTIONS Fall 2005 = (1)3+1 0 1 1 2 2 2 + (1)3+3 (1) + (1)3+2 1 2 2 3 1 3 2 1 = 0 (1 3 2 2) (1 (1) 2 (2) = 3 + 4 + 1 4 = 2. 3.2 #1a. False. For example, the determinant of a 2

• Georgia Tech MATH 1522
MATH 1522 SELECTED CHAPTER #2 SOLUTIONS Fall 2005 2.1 #42. a. Were given that v1 people live in the city and v2 people live in the suburbs. Were told that 60% of the city dwellers drive cars and 30% of the suburb dwellers drive cars. Therefore, th

• Georgia Tech MATH 1522
MATH 1522 SELECTED CHAPTER #6 SOLUTIONS Fall 2005 6.1 #49. Prove the Parallelogram Law for vectors in Rn : u+v Solution u+v 2 2 + uv 2 = 2 u 2 + v 2 . + uv 2 = (u + v) (u + v) + (u v) (u v) = uu+uv+vu+vv+uuuvvu+vv = uu+vv+uu+vv = 2

• Georgia Tech MATH 1522

• Georgia Tech MATH 1522
MATH 1522 C QUIZ #4 NAME: November 18, 2005 Answer the following questions clearly and completely. 3 8 0 (10 points) 1. Let A = 4 9 0 . Is A diagonalizable? If yes, nd an invertible 0 0 5 matrix P and a diagonal matrix D such that A = P DP 1 (yo

• Georgia Tech MATH 1522
MATH 1522 C When and Where QUIZ #2: INSTRUCTIONS September 23, 2005 The quiz will take place in the last 20 minutes of class on Friday, September 23, 2005. The quiz will take place in our regular classroom, Skiles 146. What to Bring (and Not t

• Georgia Tech MATH 1522
MATH 1522 C When and Where QUIZ #5: INSTRUCTIONS December 2, 2005 The quiz will take place in the last 20 minutes of class on Friday, December 2, 2005. The quiz will take place in our regular classroom, Skiles 146. What to Bring (and Not to Br

• Georgia Tech MATH 1522

• Georgia Tech MATH 1522

• Georgia Tech MATH 1522
MATH 1522 Section M September 22, 2008 \"PRACTICE EXAM 1\" Name: gtID#: Note: The exam is worth 100 points and there are five problems. Write out your solutions neatly and explain your work. The use of calculators is not allowed. Problem 1 (14 point

• Georgia Tech MATH 1522
MATH 1522 When and Where EXAM #1: INSTRUCTIONS September 9, 2005 The exam starts sharply at 10:05 a.m. on Friday, September 9. Please arrive by 10:00. The exam will take place in our regular classroom, Skiles 146. What to Bring (and Not to Bring) Calcula

• Georgia Tech MATH 1522
MATH 1522 When and Where EXAM #3: INSTRUCTIONS November 11, 2005 The date of this exam has been RESCHEDULED to November 11, 2005. The exam starts sharply at 10:05 a.m. on Friday, November 11. Please arrive by 10:00. The exam will take place in our regula

• Georgia Tech MATH 1522
MATH 1522 C When and Where QUIZ #4: INSTRUCTIONS November 18, 2005 The quiz will take place in the last 20 minutes of class on Friday, November 18, 2005. The quiz will take place in our regular classroom, Skiles 146. What to Bring (and Not to Bring) Calc

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