Most Popular Algebra Documents
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Quiz 3 Solution
School: Ohio State University
Course: MATH 2568
... Lecturer: Gangyong Lee Time:_____ Jan. 28, 2013 ID#_____ 1. Let A = ⎡ ⎣ 3 1 1 4 7 2 2 4 3 ⎤ ⎦ and v = ⎡ ⎣ 1 -2 3 ⎤ ⎦. Calculate the scalar of the following: ||vT Av||. (8 points.) Sol) vT Av = [1 -2 3] ⎡ ⎣ 3 1 1 4 7 2 2 4 3...
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1 Page
Quiz 11 Solution
School: Ohio State University
Course: MATH 2568
Math 2568 Quiz XI Solution Name:_____ Lecturer: Gangyong Lee Time:_____ April 22, 2013 ID#_____ (a)-(b) Let A = [4 0 5 0 3 -2 0 4 -1 ] be a matrix. (a) Find the characteristic polynomial and the eigenvalues for A. (8 pts.) Sol) det(A - λI) = ∣ ...
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1 Page
Quiz 4 Solution
School: Ohio State University
Course: MATH 2568
Math 2568 Quiz IV Solution Name:_____ Lecturer: Gangyong Lee Time:_____ Feb. 11, 2013 ID#_____ 1. Find (1) u + 2v and (2) a vector w such that u + 2w = v where u = −5i + 7k and v = −3j + k. (10 points.) Sol) (1) u + 2v = −5i + 7k − 6j + 2k...
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1 Page
Quiz 1 Solution
School: Ohio State University
Course: MATH 2568
Math 2568 Quiz I Solution Name:_____ Lecturer: Gangyong Lee Time:_____ Jan. 11, 2013 ID#_____ 1. Display the coefficient matrix A and the augmented matrix B. (6 points.) y -3z = -1 x +2y -5z = -2 -x -3y +7z = 3 Sol) A = ⎡ ⎣ 0 1 -3 1 2 -5 -1 -3...
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School: Liberty University
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School: New York University
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probability homework 2 Jiawei Sun Exercise 1 1 If is an innite countable set, then Z, so we just need to consider = the case when = Z: Let Ai = cfw_i. Obviously, for any i, Ai A, but Ai = cfw_1, 2, 3, . A. So A is not a -algebra. ...
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School: Queens University
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Quiz 3 Solution
School: Ohio State University
Course: MATH 2568
... Lecturer: Gangyong Lee Time:_____ Jan. 28, 2013 ID#_____ 1. Let A = ⎡ ⎣ 3 1 1 4 7 2 2 4 3 ⎤ ⎦ and v = ⎡ ⎣ 1 -2 3 ⎤ ⎦. Calculate the scalar of the following: ||vT Av||. (8 points.) Sol) vT Av = [1 -2 3] ⎡ ⎣ 3 1 1 4 7 2 2 4 3...
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1 Page
Quiz 11 Solution
School: Ohio State University
Course: MATH 2568
Math 2568 Quiz XI Solution Name:_____ Lecturer: Gangyong Lee Time:_____ April 22, 2013 ID#_____ (a)-(b) Let A = [4 0 5 0 3 -2 0 4 -1 ] be a matrix. (a) Find the characteristic polynomial and the eigenvalues for A. (8 pts.) Sol) det(A - λI) = ∣ ...
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Quiz 4 Solution
School: Ohio State University
Course: MATH 2568
Math 2568 Quiz IV Solution Name:_____ Lecturer: Gangyong Lee Time:_____ Feb. 11, 2013 ID#_____ 1. Find (1) u + 2v and (2) a vector w such that u + 2w = v where u = −5i + 7k and v = −3j + k. (10 points.) Sol) (1) u + 2v = −5i + 7k − 6j + 2k...
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1 Page
Quiz 1 Solution
School: Ohio State University
Course: MATH 2568
Math 2568 Quiz I Solution Name:_____ Lecturer: Gangyong Lee Time:_____ Jan. 11, 2013 ID#_____ 1. Display the coefficient matrix A and the augmented matrix B. (6 points.) y -3z = -1 x +2y -5z = -2 -x -3y +7z = 3 Sol) A = ⎡ ⎣ 0 1 -3 1 2 -5 -1 -3...
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Quiz10 Solutions
School: University Of Michigan
Course: MATH 217
Math 217 003 - Winter 2015 Quiz 10 Solutions 3 2 4 1. (3 points) Let A = 0 1 0 . It has = 1 as an eigenvalue. Find all eigenvalues of A and 2 5 3 the algebraic and geometric multiplicities of each eigenvalue. Is A diagonalizable? Justify all your ...
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linear_algebra_midterm_01_v7_solutions
School: University Of Ontario Institute Of Technology
Course: MATH 2050U
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School: University Of Michigan
Course: MATH 217
... positive integer n, the set H of n × n matrices with determinant equal to 0 is a subspace of the vector space Mn×n of all n × n matrices. Math 217 Midterm 1, Page 7 of 7 7. (8 points) Prove that if T : Rn → Rn is a linear function and ...
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School: University Of Michigan
Course: MATH 217
Math 217 - Spring 2014 Quiz 1 Solutions 1. (7 points) Perform Gauss Jordan elimination on the augmented matrix to solve the following linear system ... Show that T is a linear transformation and find its matrix. Solution : Let ...
