How do you get the linear combination? I don't get how for x2 you get [2100], for x3 you get [-1010] and for x4 you get [-3001]. Please explain that in detail. 10LO-2 1 370000 0 0]X1x2x3XAFrom this matrix, we get the equation,x₁ - 2x₂ + x3 + 3x4 = 0which we can solve for the single pivot variable.x₁ = 2x2-x3-3x4x1We can rewrite this as a linear combination.[]0= x₂x2x32100X4+x3+ x400

Answered: Image /qna-images/answer/93532d06-a7f2-4ccb-9480-ee0a7939ed23.jpg

1 -2 1 37 00 00 Lo 0 00 X1 x2 x3 ХА [x₁ x2 x3 X4 From this matrix, we get the equation, x₁2x₂ + x3 + 3x4 = 0 which we can solve for the single pivot variable. x₁ = 2x₂ - x3 - 3x4 = x₂ x2 2 1 0 We can rewrite this as a linear combination. 0 ] 1 0 = [] 0 +x3 + x4 3 0 ģ 0

1 -2 1 37 00 00 Lo 0 00 X1 x2 x3 ХА [x₁ x2 x3 X4 From this matrix, we get the equation, x₁2x₂ + x3 + 3x4 = 0 which we can solve for the single pivot variable. x₁ = 2x₂ - x3 - 3x4 = x₂ x2 2 1 0 We can rewrite this as a linear combination. 0 ] 1 0 = [] 0 +x3 + x4 3 0 ģ 0

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CR: Review Exercises

Problem 59CR

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Question

100%

How do you get the linear combination? I don't get how for x2 you get [2100], for x3 you get [-1010] and for x4 you get [-3001]. Please explain that in detail.

1
0
LO
-2 1 37
0
00
0 0 0]
X1
x2
x3
XA
From this matrix, we get the equation,
x₁ - 2x₂ + x3 + 3x4 = 0
which we can solve for the single pivot variable.
x₁ = 2x2-x3-3x4
x1
We can rewrite this as a linear combination.
[]
0
= x₂
x2
x3
2
1
0
0
X4
+x3
+ x4
0
0

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