Consider the matrices A = 1 1 [f] U = g h O V = 1 b b X 0 dB = 0 [f a 1 d g 1 C h 0 and X = y. If AX= U has infinitely 0 Z many solutions, then prove that BX= V has no unique solution. Also, show that if afd = 0, then BX = V has no solution.
Consider the matrices A = 1 1 [f] U = g h O V = 1 b b X 0 dB = 0 [f a 1 d g 1 C h 0 and X = y. If AX= U has infinitely 0 Z many solutions, then prove that BX= V has no unique solution. Also, show that if afd = 0, then BX = V has no solution.
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
![Consider the matrices A = | 1
1
[f]
U = g
h
V =
O
0
0
1
b
b
0
a
d. B = 0
[f
C
1
d
g
1
C
h
X
and X = y. If AX= U has infinitely
Z
many solutions, then prove that BX= Vhas no unique solution.
Also, show that if afd # 0, then BX = V has no solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57d0d76f-4d90-4acd-860a-2f3b7764011d%2F30b2dbd4-4d43-42ce-9e00-876cf93266e4%2Fqvnyzsx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the matrices A = | 1
1
[f]
U = g
h
V =
O
0
0
1
b
b
0
a
d. B = 0
[f
C
1
d
g
1
C
h
X
and X = y. If AX= U has infinitely
Z
many solutions, then prove that BX= Vhas no unique solution.
Also, show that if afd # 0, then BX = V has no solution.
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