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All vectors and subspaces are in R". Note you only have 5 attempts for this question. Check the true statements below: > A. If 2 is orthogonal to ₁ and 2 and if W-span(1, 2), then z must be in W B. For each and each subspace W, the vector y - projw() is orthogonal to W. C. If y is in a subspace W, then the orthogonal projection of y onto W is y itself. D. If a matrix A is such that AT = A then the perpendicular complement of the kernel of A is the image of A. ->> E. The orthogonal projection of y onto a subspace W can sometimes depend on the matrix used to compute. F. If ý = Z1 + Z2, where ž₁ is in a subspace W and 22 is in W, then 2₁ must be the orthogonal projection of y onto W. G. The closest vector to y in a subspace W is given by the vector y – projw(y). H. The columns of a matrix A are perpendicular to the rows of AT I. If W is a subspace and if ₹ is in both W and W, then must be the zero vector.

All vectors and subspaces are in R". Note you only have 5 attempts for this question. Check the true statements below: > A. If 2 is orthogonal to ₁ and 2 and if W-span(1, 2), then z must be in W B. For each and each subspace W, the vector y - projw() is orthogonal to W. C. If y is in a subspace W, then the orthogonal projection of y onto W is y itself. D. If a matrix A is such that AT = A then the perpendicular complement of the kernel of A is the image of A. ->> E. The orthogonal projection of y onto a subspace W can sometimes depend on the matrix used to compute. F. If ý = Z1 + Z2, where ž₁ is in a subspace W and 22 is in W, then 2₁ must be the orthogonal projection of y onto W. G. The closest vector to y in a subspace W is given by the vector y – projw(y). H. The columns of a matrix A are perpendicular to the rows of AT I. If W is a subspace and if ₹ is in both W and W, then must be the zero vector.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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All vectors and subspaces are in R". Note you only have 5 attempts for this question. Check the true statements below: > A. If 2 is orthogonal to ₁ and 2 and if W-span(1, 2), then z must be in W B. For each and each subspace W, the vector y - projw() is orthogonal to W. C. If y is in a subspace W, then the orthogonal projection of y onto W is y itself. D. If a matrix A is such that AT = A then the perpendicular complement of the kernel of A is the image of A. ->> E. The orthogonal projection of y onto a subspace W can sometimes depend on the matrix used to compute. F. If ý = Z1 + Z2, where ž₁ is in a subspace W and 22 is in W, then 2₁ must be the orthogonal projection of y onto W. G. The closest vector to y in a subspace W is given by the vector y – projw(y). H. The columns of a matrix A are perpendicular to the rows of AT I. If W is a subspace and if ₹ is in both W and W, then must be the zero vector.
Transcribed Image Text:All vectors and subspaces are in R". Note you only have 5 attempts for this question. Check the true statements below: > A. If 2 is orthogonal to ₁ and 2 and if W-span(1, 2), then z must be in W B. For each and each subspace W, the vector y - projw() is orthogonal to W. C. If y is in a subspace W, then the orthogonal projection of y onto W is y itself. D. If a matrix A is such that AT = A then the perpendicular complement of the kernel of A is the image of A. ->> E. The orthogonal projection of y onto a subspace W can sometimes depend on the matrix used to compute. F. If ý = Z1 + Z2, where ž₁ is in a subspace W and 22 is in W, then 2₁ must be the orthogonal projection of y onto W. G. The closest vector to y in a subspace W is given by the vector y – projw(y). H. The columns of a matrix A are perpendicular to the rows of AT I. If W is a subspace and if ₹ is in both W and W, then must be the zero vector.
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