13. (Strang 4.3.28) Suppose that the columns of A are not linearly independant.(a) Explain why P = A(AT A)-1AT is not the matrix that gives the projection onto thecolumn space of A.B(B™ B)-'B" does give the(b) How could you construct a matrix B such that Pprojection onto colsp(A)?!!

Answered: Image /qna-images/answer/bf7d03ab-935e-4930-91bd-34933f71d952.jpg

Answered: Strang 4.3.28) Suppose that the columns…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Strang 4.3.28) Suppose that the columns of A are not linearly independant. a) Explain why P = A(AT A)-AT is not the matrix that gives the projection onto the column space of A. b) How could you construct a matrix B such that P = B(B" B)-'B" does give the projection onto colsp(A)?