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 = I 12 00 12 12 0 12 12 12 12 000 12 12 0 0 12 12 12 0 12 12 12 12 1 12 12 0 0 0 1 12 1 12 12 12 (Type an integer or simplified fraction for each matrix element.) 1 0 12 1 12 0 1_2_1_12 1 12 0 0... 1 12 0 0 0 1 1 12 12 (Type an integer or simplified fraction for each matrix element.) If A is the corresponding nxn matrix and B is its inverse, which of the following is B? O A. 1 0 1 0 1 0 0 0... 0 0 1 12 1 12 0 0 0 0 1 12 00 0 0 1 12 0 OB. 1 72 0 0... 1 0 # 12 1 0 12 12 -2 -2 -12-12 000... 00 00 0 0 1 12 12 00 12 12 0 12 12 12 and 12 000 12 12 00 12 12 12 0 12 12 12 12
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 = I 12 00 12 12 0 12 12 12 12 000 12 12 0 0 12 12 12 0 12 12 12 12 1 12 12 0 0 0 1 12 1 12 12 12 (Type an integer or simplified fraction for each matrix element.) 1 0 12 1 12 0 1_2_1_12 1 12 0 0... 1 12 0 0 0 1 1 12 12 (Type an integer or simplified fraction for each matrix element.) If A is the corresponding nxn matrix and B is its inverse, which of the following is B? O A. 1 0 1 0 1 0 0 0... 0 0 1 12 1 12 0 0 0 0 1 12 00 0 0 1 12 0 OB. 1 72 0 0... 1 0 # 12 1 0 12 12 -2 -2 -12-12 000... 00 00 0 0 1 12 12 00 12 12 0 12 12 12 and 12 000 12 12 00 12 12 12 0 12 12 12 12
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:Use the algorithm for finding A¹ 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 = I.
12 00
12 12 0
12 12 12
12 0 0 0
12 12 0
0
12 12 12 0
12 12 12 12
1
12
1
0
=
17/122
1
12
1
12 12
(Type an integer or simplified fraction for each matrix element.)
1
1_12_1_12
0 0...
1
12
0
000
1
12
1
12
0
12
0
0
0
0
0
1
A
1 1
12
12
(Type an integer or simplified fraction for each matrix element.)
If A is the corresponding nxn matrix and B is its inverse, which of the following is B?
O A.
1
12
0
0
1
12
1
12 12
0
0
0
1
1
12 12
0 0
00
0 0
1
-In
- 10
0
C
O B.
1
0... 00
12
1
1
0
0 0
12 12
5
1 1
0
00
12 12
1 1
00...
12 12
12 0 00
12 12 0
12 12 12
and
12 000
12 12 0 0
12 12 12 0
12 12 12 12
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