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Consider the linear system 3x1 -6x2 +3r3 +9x4 3 %3D 2x1 -3x2 +3x3 +4x4 4 %3D -3x1 +7x2 -2xz -10x4 -1 %3D 1 -2 1 3 1 The REF of the augmented matrix is: 1 1 2 2 1 0 OTrue OFalse T1 and æ4 are the leading variables, while r2 and æ3 are the free variables OTrue OFalse The solution set is {(5 – 3a, a, 2 – a, 0), Va e R} OTrue OFalse

Consider the linear system 3x1 -6x2 +3r3 +9x4 3 %3D 2x1 -3x2 +3x3 +4x4 4 %3D -3x1 +7x2 -2xz -10x4 -1 %3D 1 -2 1 3 1 The REF of the augmented matrix is: 1 1 2 2 1 0 OTrue OFalse T1 and æ4 are the leading variables, while r2 and æ3 are the free variables OTrue OFalse The solution set is {(5 – 3a, a, 2 – a, 0), Va e R} OTrue OFalse

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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Are the three statements true or false?

Consider the linear system 3x1 -6x2 +3x3 +9x4 3 %3D 2a1 -3x2 +3x3 +4x4 4 %3D -3x1 +7x2 -2xz -10x4 -1 %3! 3 1 2 2 1 -2 1 The REF of the augmented matrix is: 1 1 1 OTrue OFalse a1 and r4 are the leading variables, while x2 and x3 are the free variables Оrue OFalse The solution set is {(5 – 3a, a, 2 – a, 0), Va e R} OTrue OFalse IL ||
Transcribed Image Text:Consider the linear system 3x1 -6x2 +3x3 +9x4 3 %3D 2a1 -3x2 +3x3 +4x4 4 %3D -3x1 +7x2 -2xz -10x4 -1 %3! 3 1 2 2 1 -2 1 The REF of the augmented matrix is: 1 1 1 OTrue OFalse a1 and r4 are the leading variables, while x2 and x3 are the free variables Оrue OFalse The solution set is {(5 – 3a, a, 2 – a, 0), Va e R} OTrue OFalse IL ||
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