In Exercises 15-20, W is a subspace of R4 consisting of vectors of the form X = XI X2 X3 X4 Determine dim(W) when the components of x satisfy the given conditions. 15. x₁ - 2x₂ + x3 x4 = 0
In Exercises 15-20, W is a subspace of R4 consisting of vectors of the form X = XI X2 X3 X4 Determine dim(W) when the components of x satisfy the given conditions. 15. x₁ - 2x₂ + x3 x4 = 0
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 10EQ
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![In Exercises 15-20, W is a subspace of R4 consisting of
vectors of the form
X =
15. x1
-2x2 + x3
16. x₁ - 2x3 = 0
XI
X2
Determine dim(W) when the components of x satisfy
the given conditions.
17. x₁ = x₂ + 2x4
==
x3 =
- X4
X3
X4
x4 = 0
18. x1
+ x3
x2 + 2x3
2x40
3x4 = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb6f2855f-e2e4-4187-86ac-8a1d153cf710%2Fee342512-c63a-4490-aeb8-220a25a14847%2F7ugw2dd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In Exercises 15-20, W is a subspace of R4 consisting of
vectors of the form
X =
15. x1
-2x2 + x3
16. x₁ - 2x3 = 0
XI
X2
Determine dim(W) when the components of x satisfy
the given conditions.
17. x₁ = x₂ + 2x4
==
x3 =
- X4
X3
X4
x4 = 0
18. x1
+ x3
x2 + 2x3
2x40
3x4 = 0
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