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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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 35EQ
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Linear algebra: please solve q6 and 8 correctly and handwritten. Please solve both
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
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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