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3. Consider the vectors 1 W1 E W2 = and the subspace W = span{w₁, W2, W3} CR¹. (a) Find an orthogonal basis for W. W3 = 0

3. Consider the vectors 1 W1 E W2 = and the subspace W = span{w₁, W2, W3} CR¹. (a) Find an orthogonal basis for W. W3 = 0

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 38EQ
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3. Consider the vectors 1 W1 O |H| W2 = 0 and the subspace W = span{w₁, W2, W3} CR¹. (a) Find an orthogonal basis for W. (b) Find an orthogonal basis for W¹. (c) Compute the orthogonal projection of e₁ onto W. (d) Find the distance between ₁ and W. (e) Find the distance between e₁ and W-. (f) Compute the matrix of the linear map projw: R4 → R4 with respect to the basis (b₁,..., b4), where the b; are the basis vectors computed in (3a) and (3b). (g) Compute the matrix of the linear map projw₁ : R4 → R4 with respect to the basis (b₁,..., b4), where the b; are the basis vectors computed in (3a) and (3b). W3 =
Transcribed Image Text:3. Consider the vectors 1 W1 O |H| W2 = 0 and the subspace W = span{w₁, W2, W3} CR¹. (a) Find an orthogonal basis for W. (b) Find an orthogonal basis for W¹. (c) Compute the orthogonal projection of e₁ onto W. (d) Find the distance between ₁ and W. (e) Find the distance between e₁ and W-. (f) Compute the matrix of the linear map projw: R4 → R4 with respect to the basis (b₁,..., b4), where the b; are the basis vectors computed in (3a) and (3b). (g) Compute the matrix of the linear map projw₁ : R4 → R4 with respect to the basis (b₁,..., b4), where the b; are the basis vectors computed in (3a) and (3b). W3 =
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