Q-1: Answer each of the following as True or False justifying your answers: a) If A = ; , then A100 , b) For any three matrices A, B and C, if AB = BA and BC = CB, then AC = CA. c) If (I – 2A")-1 = [{ ) then A = d) If A and B are 4 × 4 nonsingular matrices such that |2A¬ªB²| = 32, then 1 [0 |A| = LB2 e) Let S = {(1,0,0,0), (01,0,0), (2,3,5a,0), (a, 0,2, a – 2)} be set of vectors in R*. The set S is linearly independent if and only if a + 0. %3D
Q-1: Answer each of the following as True or False justifying your answers: a) If A = ; , then A100 , b) For any three matrices A, B and C, if AB = BA and BC = CB, then AC = CA. c) If (I – 2A")-1 = [{ ) then A = d) If A and B are 4 × 4 nonsingular matrices such that |2A¬ªB²| = 32, then 1 [0 |A| = LB2 e) Let S = {(1,0,0,0), (01,0,0), (2,3,5a,0), (a, 0,2, a – 2)} be set of vectors in R*. The set S is linearly independent if and only if a + 0. %3D
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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Transcribed Image Text:Q-1: Answer each of the following as True or False justifying your answers:
100 1 11
a) If A = ; 1, then A100 = ()* ;
b) For any three matrices A, B and C, if AB
= BA and BC = CB, then AC = CA.
1 [0
1
c) If (I – 2A")-1 = then A = I:
d) If A and B are 4 x 4 nonsingular matrices such that |2A-²B²| = 32, then
|A| = B2
e) Let S = {(1,0,0,0), (01,0,0), (2,3,5a, 0), (a, 0,2, a – 2)} be set of vectors in
R*. The set S is linearly independent if and only if a + 0.
2
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