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, ±nd the inverse, or show that the matrix is not invertible. a) A = 1 - 12 315 223 . b) B = 1 - 102 0 1 1 0 2 - 235 1 0 1 3 . 2. Let B = 2 - 11 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 ±rst row and the fourth row. c) multiply the second row by 3.
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This note was uploaded on 04/30/2010 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

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