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Assignment5

# Assignment5 - Math 136 Assignment#5 1 In each part A and B...

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Math 136 Assignment #5 1. In each part, A and B are given matrices. Determine whether the matrix product AB and BA are deﬁned. If a product is deﬁned, then compute it. (a) A = ± 1 7 - 2 3 ² B = ± 2 x y 8 ² (b) A = 1 7 0 2 2 B = 0 2 5 - 1 7 11 10 3 - 4 4 1 0 0 0 - 9 (c) A = 2 a 1 b - 7 9 3 0 c B = ± 1 - 1 a b 0 - 3 ² (d) A = 1 x x 2 x 3 B = ³ x 3 x 2 x 1 ´ 2. Let A = ± 2 3 7 - 1 0 - 4 8 11 ² , B = ± 5 7 - 2 10 - 1 0 1 - 3 ² , r = 3, and s = - 2. Compute the following. (a) rA + sB (b) B + 0 where 0 is the 2 × 4 zero matrix. (c) ( r - s )( A - B ) (d) B 0 where 0 is the 4 × 2 zero matrix. What is the size of the product B 0? (e) r ( sA ) + ( sr ) B 3. Let A be an m × n matrix and B be an n × p matrix. We write ( a ij ) to denote the matrix A and a ij to denote the single element of A in the i th row and j th column. Similarly for B = ( b ij ). (a) If the

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Assignment5 - Math 136 Assignment#5 1 In each part A and B...

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