In the context of a 3 x 4 matrix, write down elementary matrices for the following operations: (a) c₁ - 2c4 i.e., subtract 2 times column 4 from column 1 (b) 8c3 i.e., multiply column 3 by 8 (you may assume that 20 in the field, in which case 8 + 0 also) (c) Interchange row 2 and row 3 (d) r₂ + 3r₁ i.e., add 3 times row 1 to row 2
In the context of a 3 x 4 matrix, write down elementary matrices for the following operations: (a) c₁ - 2c4 i.e., subtract 2 times column 4 from column 1 (b) 8c3 i.e., multiply column 3 by 8 (you may assume that 20 in the field, in which case 8 + 0 also) (c) Interchange row 2 and row 3 (d) r₂ + 3r₁ i.e., add 3 times row 1 to row 2
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
![In the context of a 3 x 4 matrix, write down elementary matrices for the following operations:
(a) c₁ - 2c4 i.e., subtract 2 times column 4 from column 1
(b) 8c3 i.e., multiply column 3 by 8 (you may assume that 20 in the field, in which case 8 0 also)
(c) Interchange row 2 and row 3
(d) r₂ + 3r₁ i.e., add 3 times row 1 to row 2
Select one:
(a):
(a):
(a):
1 0 0
3 1 0
0 1 0
(a):
1 0 0
0 1 0
-2 0 1
None of the others apply
"
1
0
0
-2
(b):
1
0 0 -27
0
1 0
0
0 0 1 0
0
0 0 1
0 0 01
1 00
0 1 0
00 1
(b):
¯1
0
0
0
(b) :
(b):
0 0 0
800
01 0
0 0 1
1 0 0 0
0 1 0 0
00 8 0
1 0
0
0
80
0 1
"
"
3
1 0 0 0
0 1
0 0
0 0
8
0
0
0
0 1
(c) :
(c):
(c) :
0 1 0
1
00
0 0 1
(c):
1 0 0
00 1
0 1 0]
1 0 0
00 0
0 0 1
01 0
9
1 0
0 0
0 1
"
(d):
01
1
0
0
0]
1
0
(d):
3
"
1 0 0 0
3 1 00
001 0
000 1
(d):
(d):
1 00 01
1 00
3
0 0 1 0
0 0 0 1]
1 3
0 10
0 0 1
1 0
3 1 0
0 0 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0de9773e-39c1-4df6-a7d6-864501c7f552%2F52393a58-174b-47ed-b063-4cf82f6aa5bf%2F6jj0u2o_processed.png&w=3840&q=75)
Transcribed Image Text:In the context of a 3 x 4 matrix, write down elementary matrices for the following operations:
(a) c₁ - 2c4 i.e., subtract 2 times column 4 from column 1
(b) 8c3 i.e., multiply column 3 by 8 (you may assume that 20 in the field, in which case 8 0 also)
(c) Interchange row 2 and row 3
(d) r₂ + 3r₁ i.e., add 3 times row 1 to row 2
Select one:
(a):
(a):
(a):
1 0 0
3 1 0
0 1 0
(a):
1 0 0
0 1 0
-2 0 1
None of the others apply
"
1
0
0
-2
(b):
1
0 0 -27
0
1 0
0
0 0 1 0
0
0 0 1
0 0 01
1 00
0 1 0
00 1
(b):
¯1
0
0
0
(b) :
(b):
0 0 0
800
01 0
0 0 1
1 0 0 0
0 1 0 0
00 8 0
1 0
0
0
80
0 1
"
"
3
1 0 0 0
0 1
0 0
0 0
8
0
0
0
0 1
(c) :
(c):
(c) :
0 1 0
1
00
0 0 1
(c):
1 0 0
00 1
0 1 0]
1 0 0
00 0
0 0 1
01 0
9
1 0
0 0
0 1
"
(d):
01
1
0
0
0]
1
0
(d):
3
"
1 0 0 0
3 1 00
001 0
000 1
(d):
(d):
1 00 01
1 00
3
0 0 1 0
0 0 0 1]
1 3
0 10
0 0 1
1 0
3 1 0
0 0 1
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Step 1: Formation of elementary matrix
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