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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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 Spring '08
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 Linear Algebra, Algebra, Multiplication, Matrices

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