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Question 1. Suppose v and w are two vectors in Rd. Projection of v onto w is the following vector •₁ and ||w||2 where (v, w) = vw and ||-|| is its associated norm. Compute the following the projections of the first vector to the second vector in each case: •H OND and 8 PRO 8 (v, w) W (w, w) 2 and 0 -W; Compute the projection of the projection vectors in each case? [100] Let P₁ = 000 and assume x = 000 P₁P₁X. 00 Consider now P₂ := 0 1 0 000 Compute P₁x and Do you see a pattern?

Question 1. Suppose v and w are two vectors in Rd. Projection of v onto w is the following vector •₁ and ||w||2 where (v, w) = vw and ||-|| is its associated norm. Compute the following the projections of the first vector to the second vector in each case: •H OND and 8 PRO 8 (v, w) W (w, w) 2 and 0 -W; Compute the projection of the projection vectors in each case? [100] Let P₁ = 000 and assume x = 000 P₁P₁X. 00 Consider now P₂ := 0 1 0 000 Compute P₁x and Do you see a pattern?

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 1AEXP
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Question 1. Suppose v and w are two vectors in Rd. Projection of v onto w is the following vector B and and where (v, w) = vw and ||-|| is its associated norm. Compute the following the projections of the first vector to the second vector in each case: 2 and 0 0 (v, w) (w, w) 000 P₁P₁x. Consider now P₂ -W (v.w). ||w||2W Compute the projection of the projection vectors in each case? [100] Let P₁000 and assume x = 00 0 1 0 000 -W; Do Compute P₁x and you see a pattern?
Transcribed Image Text:Question 1. Suppose v and w are two vectors in Rd. Projection of v onto w is the following vector B and and where (v, w) = vw and ||-|| is its associated norm. Compute the following the projections of the first vector to the second vector in each case: 2 and 0 0 (v, w) (w, w) 000 P₁P₁x. Consider now P₂ -W (v.w). ||w||2W Compute the projection of the projection vectors in each case? [100] Let P₁000 and assume x = 00 0 1 0 000 -W; Do Compute P₁x and you see a pattern?
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