1. (a) Consider the matrices A = 2 3] 5 789 [1 4 6 and B = 21 0 without finding the product AB, find the following. (i) row 2 of AB (ii) column 4 of AB -1 3 1 3 6 -1 2 2 1 3 (iii) (AB)31, the entry in row 3 and column 1 of AB. r
1. (a) Consider the matrices A = 2 3] 5 789 [1 4 6 and B = 21 0 without finding the product AB, find the following. (i) row 2 of AB (ii) column 4 of AB -1 3 1 3 6 -1 2 2 1 3 (iii) (AB)31, the entry in row 3 and column 1 of AB. r
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
![1. (a) Consider the matrices A:
(b) For matrices A
-
4
7 8 9
without finding the product AB, find the following.
(i) row 2 of AB
(ii) column 4 of AB
compute following
(i) AB and BA
[12
-2
2
5 6 and B =
B
=
-2 3
3 1
0
products if they exist.
(ii) BC and CB
"
2
1
0
C
-1
1
-1
3 6
2 1 3
-[-3²
(iii) (AB)31, the entry in row 3 and column 1 of AB.
3],
(iii) CD and DC
-2 1
0 -2
and D =
3
1
1
-2
0
2
(iv) verify A(BC) = (AB)C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89b1189c-c32b-4144-b592-a832138b3e54%2F912a15f7-459a-4a2e-affa-87d2684b1809%2Fni28ril_processed.png&w=3840&q=75)
Transcribed Image Text:1. (a) Consider the matrices A:
(b) For matrices A
-
4
7 8 9
without finding the product AB, find the following.
(i) row 2 of AB
(ii) column 4 of AB
compute following
(i) AB and BA
[12
-2
2
5 6 and B =
B
=
-2 3
3 1
0
products if they exist.
(ii) BC and CB
"
2
1
0
C
-1
1
-1
3 6
2 1 3
-[-3²
(iii) (AB)31, the entry in row 3 and column 1 of AB.
3],
(iii) CD and DC
-2 1
0 -2
and D =
3
1
1
-2
0
2
(iv) verify A(BC) = (AB)C.
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