Use the algorithm for finding A to find the inverses of the matrices shown to the right. Let A be the corresponding nxn matrix, and let B be its inverse. Guess the form of B, and then show that AB = 1. 1000 100 1100 110 and 1110 11 1111 100 1 10 1000 1100 1110 11 OOOC OOOC

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.3: The Inverse Of A Matrix
Problem 79E: Let A,D, and P be nn matrices satisfying AP=PD. Assume that P is nonsingular and solve this for A....
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If A is the corresponding nxn matrix and B is its inverse, which of the following is B?
A.
ов.
1
1
0 0
0 0
...
...
1 - 1
- 1
1 0
0 0
1
- 1
0 - 1 1
0 0
... 1 - 1
0 0
-1 1
...
For j= 1,2,..,n, let a;, b;, and
ej
denote the jth columns of A, B, and I, respectively. Evaluate Ab;.
Ab; =
Rewrite without parentheses.
Multiply.
%3D
Because the result from the previous step is equal to
V it follows that AB = 1.
O . . . O
Transcribed Image Text:If A is the corresponding nxn matrix and B is its inverse, which of the following is B? A. ов. 1 1 0 0 0 0 ... ... 1 - 1 - 1 1 0 0 0 1 - 1 0 - 1 1 0 0 ... 1 - 1 0 0 -1 1 ... For j= 1,2,..,n, let a;, b;, and ej denote the jth columns of A, B, and I, respectively. Evaluate Ab;. Ab; = Rewrite without parentheses. Multiply. %3D Because the result from the previous step is equal to V it follows that AB = 1. O . . . O
Use the algorithm for finding A to find the inverses of the matrices shown to the right. Let A be the corresponding nxn matrix, and let B be its inverse. Guess the form of B, and then show that AB = 1.
1000
100
1100
110 and
1110
111
1111
100
110
1000
1100
1110
11
OOOD
Transcribed Image Text:Use the algorithm for finding A to find the inverses of the matrices shown to the right. Let A be the corresponding nxn matrix, and let B be its inverse. Guess the form of B, and then show that AB = 1. 1000 100 1100 110 and 1110 111 1111 100 110 1000 1100 1110 11 OOOD
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