[1 8. Let P = I=0 0 0 [1 0 1 0 P, =0 1 0 0 1 1 0j [o 1 0] 1 0 0 [o 1 0 P, =1 P = 0 0 0 | 1 0 0 0 0 0 1 P, =1 0 0 0 1 P. =0 1 0 1 0 0

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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[1 0 0
1 0
8. Let P = I =0
1
0.
P, =
1
%3D
[0 0 1|
1 0
[0 1
[o 1
P, =| 1
P4 =0
1
%3D
0.
1 |
0 0
1
0 0
P3
10 0
P.
0.
%3D
1
1
[2 1
31
and X = P.10 2 P!
k = 1
3 2 1
where, P denotes the transpose of the matrix P. Then
which of the following option is/are correct?
(a) X is a symmetric matrix
(b) The sum of diagonal entries of X is 18
(c) X- 30/ is an invertible matrix
[1]
(d) If X 1
= a 1 then a = 30
1
1.
Transcribed Image Text:[1 0 0 1 0 8. Let P = I =0 1 0. P, = 1 %3D [0 0 1| 1 0 [0 1 [o 1 P, =| 1 P4 =0 1 %3D 0. 1 | 0 0 1 0 0 P3 10 0 P. 0. %3D 1 1 [2 1 31 and X = P.10 2 P! k = 1 3 2 1 where, P denotes the transpose of the matrix P. Then which of the following option is/are correct? (a) X is a symmetric matrix (b) The sum of diagonal entries of X is 18 (c) X- 30/ is an invertible matrix [1] (d) If X 1 = a 1 then a = 30 1 1.
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