assignment4_solutions - MATH 1300 ASSIGNMENT PROBLEMS(UNIT...

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MATH 1300 ASSIGNMENT PROBLEMS (UNIT 4) Solutions [10] 1. Let 2 1 3 A = 4 0 1 3 5 2 and let B = 5 3 1 2 4 3 1 2 0 . Find the following. (a) T A+2B (b) AB (c) BA (d) The matrix C for which 2A + T C = B. Solution : (a) A + B = 2 1 3 10 4 2 12 3 5 4 0 1 6 8 4 10 8 3 3 5 2 2 6 0 1 11 2 + = (b) AB = 2 1 3 5 3 1 11 4 5 4 0 1 2 4 3 21 10 4 3 5 2 1 2 0 23 33 12     =       (c) BA = 5 3 1 2 1 3 19 10 20 2 4 3 4 0 1 27 13 4 1 2 0 3 5 2 6 1 1     =       (d) T 5 3 1 4 2 6 1 5 7 C B 2A 2 4 3 8 0 2 6 4 1 1 2 0 6 10 4 5 12 4 =− = =− C = 1 6 5 5 4 12 7 1 4
[10] 2.(a) Which of the following matrices are elementary matrices?
(c) Let A = 2 1 1 0 . Find two elementary matrices E 1 and E 2 such that E 2 E 1 A = I. Solution :

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