a) If A and B are 5 x 5 matrices such that AB = -BA, then AB is singular. b) If (AB)? = A²B², then AB = c) If A is ann X n matrix such that A² |C1 + 2a1 bị a1 = |C3 + 2a3 b3 az |c2 + 2a2 b2 az ВА. 0, then (I – A)-1 = I + A. |a1 a2 az d) b1 b3 b3 |C1 C2 C3 e) The vector (1,2,0,4) is a linear combination of the vectors (1,0,1,2), (2,0,2,3) and (3,0,2,2).
a) If A and B are 5 x 5 matrices such that AB = -BA, then AB is singular. b) If (AB)? = A²B², then AB = c) If A is ann X n matrix such that A² |C1 + 2a1 bị a1 = |C3 + 2a3 b3 az |c2 + 2a2 b2 az ВА. 0, then (I – A)-1 = I + A. |a1 a2 az d) b1 b3 b3 |C1 C2 C3 e) The vector (1,2,0,4) is a linear combination of the vectors (1,0,1,2), (2,0,2,3) and (3,0,2,2).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Q−1:Answer each of the following as True or False justifying your answers:
Transcribed Image Text:a) If A and B are 5 x 5 matrices such that AB = -BA, then AB is singular.
b) If (AB)? = A²B², then AB =
c) If A is ann X n matrix such that A²
|C1 + 2a1 bị a1
= |C3 + 2a3 b3 az
|c2 + 2a2 b2 az
ВА.
0, then (I – A)-1 = I + A.
|a1
a2
az
d) b1 b3 b3
|C1
C2
C3
e) The vector (1,2,0,4) is a linear combination of the vectors (1,0,1,2), (2,0,2,3)
and (3,0,2,2).
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