Determine whether the statement below is true or false. Justify the answer. Assume all vectors and subspaces are in R". If y is in a subspace W, then the orthogonal projection of y onto W is y itself. Choose the correct answer below. O A. The statement is true. For an orthogonal basis B= (u, u) of W, y and projwy can be written as linear combinations of vectors in B with equal weights. O B. The statement is true. If y is in W, then projwyy= -y, which is in the same spanning set as y. OC. The statement is false. If y is in W, then projwy =0. This means the statement is false unless y = 0. OD. The statement is false. If y is in W, then projwy is orthogonal to y and is in wt.

Determine whether the statement below is true or false. Justify the answer. Assume all vectors and subspaces are in R". If y is in a subspace W, then the orthogonal projection of y onto W is y itself. Choose the correct answer below. O A. The statement is true. For an orthogonal basis B= (u, u) of W, y and projwy can be written as linear combinations of vectors in B with equal weights. O B. The statement is true. If y is in W, then projwyy= -y, which is in the same spanning set as y. OC. The statement is false. If y is in W, then projwy =0. This means the statement is false unless y = 0. OD. The statement is false. If y is in W, then projwy is orthogonal to y and is in wt.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 42CR: Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). Let B={(0,2,2),(1,0,2)} be a basis for a...

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