(a) Let S₁ = {(-3,0,3), (6, −4, 7), (2, 1, −3)} and S₂ = {(3, 0,3), (3, -4, −1), (1, 1, 2)}. Test each set for linear independence. Note: The vectors in the sets are column vectors. They are written in row form in order to save space. (b) Use step-by-step Gauss Elimination to solve the system. -1 3 2 0 X1 3 2 140 X2 19 -3 22 0 X3 -264 1 X4 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(a) Let S₁ = {(-3,0,3), (6, −4, 7), (2, 1, −3)} and S₂ = {(3, 0,3), (3, -4, −1), (1, 1, 2)}.
Test each set for linear independence. Note: The vectors in the sets are column
vectors. They are written in row form in order to save space.
(b) Use step-by-step Gauss Elimination to solve the system.
-1 3 2 0
X1
3
2 140
X2
19
-3 22 0
X3
-264 1
X4
3
Transcribed Image Text:(a) Let S₁ = {(-3,0,3), (6, −4, 7), (2, 1, −3)} and S₂ = {(3, 0,3), (3, -4, −1), (1, 1, 2)}. Test each set for linear independence. Note: The vectors in the sets are column vectors. They are written in row form in order to save space. (b) Use step-by-step Gauss Elimination to solve the system. -1 3 2 0 X1 3 2 140 X2 19 -3 22 0 X3 -264 1 X4 3
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