In Exercises 1-8, let W be the subspace of R4 consisting of vectors of the form Find a basis for W when the components of x satisfy the given conditions. 1. x₁ + x₂-x3 X1 X2 -B X = X3 X4 = 0 - X4 = 0 x2 2. x₁ + x₂ x3 + x4 = 0 x22x3 x4 = 0 3. x₁ - x₂ + x3 - 3x4 = 0 4. x₁x₂ + x3 = 0 5. x₁ + x₂ = 0 6. x₁-x₂ x2 - 2x3 X3 7. -x₁ + 2x₂ x2 + x3 = 0 = 0 X4 = 0 - X4 = 0 = 0 8. X₁ X2 X3 + x4 = 0 x2 + x3 = 0
In Exercises 1-8, let W be the subspace of R4 consisting of vectors of the form Find a basis for W when the components of x satisfy the given conditions. 1. x₁ + x₂-x3 X1 X2 -B X = X3 X4 = 0 - X4 = 0 x2 2. x₁ + x₂ x3 + x4 = 0 x22x3 x4 = 0 3. x₁ - x₂ + x3 - 3x4 = 0 4. x₁x₂ + x3 = 0 5. x₁ + x₂ = 0 6. x₁-x₂ x2 - 2x3 X3 7. -x₁ + 2x₂ x2 + x3 = 0 = 0 X4 = 0 - X4 = 0 = 0 8. X₁ X2 X3 + x4 = 0 x2 + x3 = 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:In Exercises 1-8, let W be the subspace of Rª consisting
of vectors of the form
Find a basis for W when the components of x satisfy the
given conditions.
1. x₁ + x₂ - X3
X2
2. x1 + x₂
XI
X2
--0
X =
X3
X4
= 0
-X4 = 0
7. -x₁ + 2x₂
x3 + x4 = 0
x4 = 0
3x4 = 0
x22x3
3. x₁x₂ + x3
4. x₁ - x₂ + x3 = 0
5. x₁ + x₂ = 0
6. x₁-x2
x2 - 2x3
X3
x2 + x3
= 0
= 0
X4 = 0
- X4 = 0
= 0
8. x₁x₂x3 + x4 = 0
x2 + x3
= 0
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