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If V is the subspace spanned by (1, 1, 0, 1) and (0, 0, 1, 0), find (a) a basis for the orthogonal complement V-L. (b) the projection matrix P onto V. (c) the vector in V closest to the vector b = (0, 1, 0, -1) in V¹. P = A(ATA)¹AT=AA¯¹(AT)-¹AT = I.

If V is the subspace spanned by (1, 1, 0, 1) and (0, 0, 1, 0), find (a) a basis for the orthogonal complement V-L. (b) the projection matrix P onto V. (c) the vector in V closest to the vector b = (0, 1, 0, -1) in V¹. P = A(ATA)¹AT=AA¯¹(AT)-¹AT = I.

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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I just need to know how to solve part b of the problem with the given equation. I tried, but I could not invert (transpose(A)*A) using online matrix invertible calculators. Can you solve part b with the equation?

If V is the subspace spanned by (1, 1, 0, 1) and (0, 0, 1, 0), find (a) a basis for the orthogonal complement V-L. (b) the projection matrix P onto V. (c) the vector in V closest to the vector b = (0, 1, 0, -1) in V¹.
Transcribed Image Text:If V is the subspace spanned by (1, 1, 0, 1) and (0, 0, 1, 0), find (a) a basis for the orthogonal complement V-L. (b) the projection matrix P onto V. (c) the vector in V closest to the vector b = (0, 1, 0, -1) in V¹.
P = A(ATA)¹AT=AA¯¹(AT)-¹AT = I.
Transcribed Image Text:P = A(ATA)¹AT=AA¯¹(AT)-¹AT = I.
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