Solve the problem. Find the general solution of the simple homogeneous "system" below, which consists of a single answer as a linear combination of vectors. Let x₂ and x3 be free variables. 2x1 - 8x2 + 6x3 = 0 x1 x2 x3 Ox1 X2 x2 = x₂ x3 O [x1 0 1 x1 x2 = 4x2 x3 x3 x2 = X₂ 1 x3 3 X30 (with X2, X3 free) X3 -3 1 (with X2, X3 free) [x1] +3x2 (with X2, X3 free) x3 +X3 -3 0 (with x2, x3 free) 1
Solve the problem. Find the general solution of the simple homogeneous "system" below, which consists of a single answer as a linear combination of vectors. Let x₂ and x3 be free variables. 2x1 - 8x2 + 6x3 = 0 x1 x2 x3 Ox1 X2 x2 = x₂ x3 O [x1 0 1 x1 x2 = 4x2 x3 x3 x2 = X₂ 1 x3 3 X30 (with X2, X3 free) X3 -3 1 (with X2, X3 free) [x1] +3x2 (with X2, X3 free) x3 +X3 -3 0 (with x2, x3 free) 1
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.CM: Cumulative Review
Problem 6CM
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![Solve the problem.
Find the general solution of the simple homogeneous "system" below, which consists of a single
answer as a linear combination of vectors. Let x₂ and x3 be free variables.
2x1 - 8x2 + 6x3 = 0
O
x2 = X2
x3
0
x2 = x₂ 0
x3
O [x1
3
+ x3 0 (with X2, X3 free)
1
x1
x2 = X₂ 1
x3
+ X3
[x1]
x2 = 4 x2 + 3x2 (with X2, X3 free)
x3
x3
x3
1 (with X2, X3 free)
0
40-4
+ X3
-3
0 (with X2, X3 free)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbeac6eb9-1fb3-41fc-a4cb-d4256681ff25%2F1119d9fe-3a8c-4df0-a6dd-99da087b0aa0%2Fou8i7qc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Solve the problem.
Find the general solution of the simple homogeneous "system" below, which consists of a single
answer as a linear combination of vectors. Let x₂ and x3 be free variables.
2x1 - 8x2 + 6x3 = 0
O
x2 = X2
x3
0
x2 = x₂ 0
x3
O [x1
3
+ x3 0 (with X2, X3 free)
1
x1
x2 = X₂ 1
x3
+ X3
[x1]
x2 = 4 x2 + 3x2 (with X2, X3 free)
x3
x3
x3
1 (with X2, X3 free)
0
40-4
+ X3
-3
0 (with X2, X3 free)
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