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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
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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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
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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