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# assign8 - Math 136 Assignment 8 Due Wednesday Mar 24th 1...

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Math 136 Assignment 8 Due: Wednesday, Mar 24th 1. For each of the following matrices, find the inverse, or show that the matrix is not invertible. a) A = 1 - 1 2 3 1 5 2 2 3 . b) B = 1 - 1 0 2 0 1 1 0 2 - 2 3 5 1 0 1 3 . 2. Let B = 2 - 1 1 0 1 1 1 - 1 - 1 . Find B - 1 and use it to solve B x = d , where d = (4 , - 2 , 3). 3. a) Prove that if A and B are n × n matrices such that AB is invertible, then A and B are invertible. b) Give an example of 2 × 3 matrix A , and 3 × 2 matrix B such that AB is invertible. Are A and B invertible? 4. Write the 4 × 4 elementary matrices that correspond to each of the following elementary row operations. a) add -2 times the third row to the second. b) interchange the first row and the fourth row. c) multiply the second row by 3. 5.
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