This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 136 Assignment 8 Solutions 1. For each of the following matrices, find the inverse, or show that the matrix is not invertible. a) A = 2 1 4 4 Solution: We have A 1 = 1 2(4) 1(4) 4 1 4 2 = 1 4 4 1 4 2 . b) B = 1 5 3 1 3 1 1 4 1 Solution: Row reducing [ B  I ] gives 1 5 3 1 0 0 1 3 1 0 1 0 1 4 1 0 0 1 1 5 3 1 2 4 1 1 3 / 2 1 / 2 1 Since the RREF of B is not I , B is not invertible. 2. Let A = 1 2 3 1 2 4 1 1 0 and B = 1 2 3 6 2 2 1 1 0 . a) Find det A and det B . Solution: We have det A = 1 2 3 1 2 4 1 1 0 = 1 3 3 1 3 4 1 0 0 = 3 det B = 1 2 3 6 2 2 1 1 0 = 3 2 3 8 2 2 0 1 0 = 18 b) Find det( AB ). Solution: det( AB ) = det A det B = 54 c) Find det( A + B ). Solution: det( A + B ) = 2 4 6 7 4 6 0 0 0 = 0 1 2 d) Find A 1 . Solution: We have 1 2 3 1 0 0 1 2 4 0 1 0 1 1 0 0 0 1 1 0 0 4 / 3 1 2 / 3 0 1 0 4 / 3 1 1 / 3 0 0 1 1 1 Thus A 1 =...
View
Full
Document
This note was uploaded on 07/13/2011 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.
 Winter '08
 All
 Math, Matrices

Click to edit the document details