M21001-HW5-2010

# M21001-HW5-2010 - MATH 21001 Spring 2010 Homework 5 Hassan...

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Unformatted text preview: MATH 21001 - Spring 2010 - Homework 5 Hassan Allouba Problem 1 When possible, find the inverse of each of the following matrices. Check your answer by using matrix multiplication. (a) 4- 8 5 4- 7 4 3- 4 2 (b) 1 1 1 1 1 2 2 2 1 2 3 3 1 2 3 4 Problem 2 Find the matrix X such that X = AX + B , where A = - 1- 1 and B = 1 2 2 1 3 3 . Problem 3 Answer each of the following questions: (a) Under what conditions is a diagonal matrix nonsingular? Describe the structure of the inverse of a diagonal matrix. (b) Under what conditions is a triangular matrix nonsingular? Describe the structure of the inverse of a triangular matrix. Problem 4 If A is nonsingular and symmetric, prove that A- 1 is symmetric. 1 Problem 5 For matrices A r × r , B s × s , and C r × s such that A and B are nonsingular, verify that each of the following is true....
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## This note was uploaded on 04/22/2010 for the course MATH 21001 taught by Professor Staff during the Spring '08 term at Kent State.

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M21001-HW5-2010 - MATH 21001 Spring 2010 Homework 5 Hassan...

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