4. Which of the following statements is/are true?hand written plz(A) For a nonzero matrix A E Rx, let P be a matrix that orthogonally projects vectorsin R" onto the column space of A. Then In- P projects onto the right null space ofA.(B) If A € R³x2 has two orthonormal columns, then ATA = 1₂.00(C) The orthogonal projection of vectors in R³ onto the column space of A02can30000be obtained by multiplying the vector with the projection matrix P = 0 0 10 1 0(D) Three orthogonal vectors in R4 can be constructed by the Gram-Schmidt procedurefrom the vectors [1,-1,0,0], [0, 1,-1,0] and [1,0,0,-1].(E) None of the above is true.

Answered: Image /qna-images/answer/dd3c96f2-5f9a-4ce9-aef6-5b27d31e7cee.jpg

of the following statements is/are true! piz (A) For a nonzero matrix A E Rx, let P be a matrix that orthogonally projects vectors in R" onto the column space of A. Then In-P projects onto the right null space of A. (B) If A € R³x2 has two orthonormal columns, then ATA = 1₂. 00 02 H can (C) The orthogonal projection of vectors in R³ onto the column space of A 30 000 be obtained by multiplying the vector with the projection matrix P == 001 0 10

of the following statements is/are true! piz (A) For a nonzero matrix A E Rx, let P be a matrix that orthogonally projects vectors in R" onto the column space of A. Then In-P projects onto the right null space of A. (B) If A € R³x2 has two orthonormal columns, then ATA = 1₂. 00 02 H can (C) The orthogonal projection of vectors in R³ onto the column space of A 30 000 be obtained by multiplying the vector with the projection matrix P == 001 0 10

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 23EQ

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