4. Which of the following statements is/are true? (A) For a nonzero matrix A E Rx, let P be a matrix that orthogonally projects vectors in R¹ 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 (C) The orthogonal projection of vectors in R³ onto the column space of A == 02 can 30 000 be obtained by multiplying the vector with the projection matrix P == 001 0 1 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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4. Which of the following statements is/are true?
(A) For a nonzero matrix A E Rnxn, 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 = I₂.
0
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 = 0 0 1
0 1 0
(D) Three orthogonal vectors in R4 can be constructed by the Gram-Schmidt procedure
from the vectors [1,-1,0,0], [0, 1,-1,0] and [1,0,0,-1].
(E) None of the above is true.
Transcribed Image Text:4. Which of the following statements is/are true? (A) For a nonzero matrix A E Rnxn, 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 = I₂. 0 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 = 0 0 1 0 1 0 (D) Three orthogonal vectors in R4 can be constructed by the Gram-Schmidt procedure from the vectors [1,-1,0,0], [0, 1,-1,0] and [1,0,0,-1]. (E) None of the above is true.
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