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

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Chapter2: Second-order Linear Odes
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Linear algebra: please solve q15, 16 and 17 correctly and handwritten

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
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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