Consider the matrices A = | 1 U = 1 0 a b b [f] g V = h a 1³-1 d, B = 0 C f 1 d g 1 C h a² X 0 and X = y. If AX = U has infinitely A 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
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Consider the matrices A =
f
U = g
h
V =
a²
a
1
1
0
d B=
=
"
a
0
f
C
1 1
d
g
C
h
b
X
and X = y. If AX= U has infinitely
0
Z
0
many solutions, then prove that BX= V has no unique solution.
Also, show that if afd # 0, then BX = V has no solution.
-
Transcribed Image Text:Consider the matrices A = f U = g h V = a² a 1 1 0 d B= = " a 0 f C 1 1 d g C h b X and X = y. If AX= U has infinitely 0 Z 0 many solutions, then prove that BX= V has no unique solution. Also, show that if afd # 0, then BX = V has no solution. -
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