In Exercises 15-20, W is a subspace of R4 consisting of vectors of the form X = X1 15. x₁ - 2x2 + x3 x4 = 0 16. x₁ - 2x3 = 0 17. x₁ = x₂ + 2x4 x3 = X4 X2 X3 Determine dim(W) when the components of x satisfy the given conditions. X4 18. X1 + x32x4 = 0 x2 + 2x3 3x4 = 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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Linear algebra: please solve q17 correctly and handwritten

In Exercises 15-20, W is a subspace of R4 consisting of
vectors of the form
X =
15. x₁ - 2x₂ + x3 x4 = 0
16. x₁ - 2x3 = 0
X1
17. x₁ = x₂ + 2x4
x3 =
- X4
X2
X3
Determine dim(W) when the components of x satisfy
the given conditions.
X4
18. XI
+ x3 2x4 = 0
x2 + 2x3 3x4 = 0
Transcribed Image Text:In Exercises 15-20, W is a subspace of R4 consisting of vectors of the form X = 15. x₁ - 2x₂ + x3 x4 = 0 16. x₁ - 2x3 = 0 X1 17. x₁ = x₂ + 2x4 x3 = - X4 X2 X3 Determine dim(W) when the components of x satisfy the given conditions. X4 18. XI + x3 2x4 = 0 x2 + 2x3 3x4 = 0
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