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14. In Exercises 15-20, W is a subspace of R* consisting of vectors of the form X = X1 X2 X3 X4 Determine dim(W) when the components of x satisfy the given conditions. 15. x₁2x2 + x3 x4 = 0 16. x₁2x3 = 0 17. x₁ = -x₂ + 2x4 x3 = - X4 18. x1 PRE + x3 - 2x4 = 0 x2 + 2x3 - 3x4 = 0

14. In Exercises 15-20, W is a subspace of R* consisting of vectors of the form X = X1 X2 X3 X4 Determine dim(W) when the components of x satisfy the given conditions. 15. x₁2x2 + x3 x4 = 0 16. x₁2x3 = 0 17. x₁ = -x₂ + 2x4 x3 = - X4 18. x1 PRE + x3 - 2x4 = 0 x2 + 2x3 - 3x4 = 0

Advanced Engineering Mathematics
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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Please answer number 17 asap!! Will rate, thanks!!!

 

14. S = In Exercises 15-20, W is a subspace of Rª consisting of vectors of the form X = 17. x₁ = x2 + 2x4 x3 = - X4 19. x₁ = -X4 x2 = 3x4 x3 = 2x4 X1 Determine dim(W) when the components of x satisfy the given conditions. 15. x₁2x2 + x3 x4 = 0 16. x₁ - 2x3 = 0 X2 X3 X4 18. x1 + x3 2x4 = 0 3x4 = 0 x2 + 2x3 20. x₁ - x2 - - =0 = 0 X3 X4 = 0 x2 - 2x3 -
Transcribed Image Text:14. S = In Exercises 15-20, W is a subspace of Rª consisting of vectors of the form X = 17. x₁ = x2 + 2x4 x3 = - X4 19. x₁ = -X4 x2 = 3x4 x3 = 2x4 X1 Determine dim(W) when the components of x satisfy the given conditions. 15. x₁2x2 + x3 x4 = 0 16. x₁ - 2x3 = 0 X2 X3 X4 18. x1 + x3 2x4 = 0 3x4 = 0 x2 + 2x3 20. x₁ - x2 - - =0 = 0 X3 X4 = 0 x2 - 2x3 -
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