Let U be the subspace of R5 deÖned by U =  (x1; x2; x3; x4; x5) 2 R5 : 2x1 = x2 and x3 = x5 : (a) Find a basis of U. (b) Find a subspace W of R5 such that R5 = U +W

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A: Let V be a vector space over a field F. A set S of vectors in V is said to be a basis of V if  (i) S…

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A: Using the Gram Schmidt orthogonalisation process:

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Q: b Ell С pts] Explain how you know that W is a subspace of R¹. er W = a+b+5c = 0, b+2c=0, a +3c+d=0

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Q: Let S = {a+bx+cx²: = {V1, V2, V3} and T a, b, c = R}, where v₁ = 1 + x + 3x², v₂ = −2 − 2x – 7x², v3…

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Q: Find a basis and state its dimension for the following subspace in Rª 3r+ 6s-t 6r-28-2t -9r+ 5s + 3t…

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A: Introduction: The coordinate vector of an element of vector space related to basis is the vector…

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A: x=(0,-1,1,-1) will be the basis, Which can be expressed as the linear combination of U, and it is…

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Q: Suppose W is the subspace of R“ satisfying the equation x1 + x2 + x3 + x4 : A. Find a basis for W-.…

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Q: Let W = Span(x₁, x₂) where and let y = -0-0 10 0 -7 1 (a) Find an orthogonal basis of W. (b) Find…

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Q: Consider the operator(function) S on the vector space R1[x] given by: S(a + bx) = -a + b + (a +…

A: see my solutiuon

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Q: Find a basis and the dimensi on of (a) U, (b) W, (c) UnW.

A: In this question, we find the basis and dimension of the subspaces and their intersections.

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A: Answer follows

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Q: Consider the subspace 3 12 3 -2 U = span{ 7 -2 -7 3 6. of R4. Create a basis 3 -2 { 3 -2 ,x} -3 for…

A: Consider the provided question, Consider the subspace U=span-3-27-7, 12-2-73, 3-2-46 of R4.Create a…