Select ALL true statements: (A) For any matrix A, we have det(A" A) > 0. (B) If M is a square matrix with QR-factorization M=QR, then det(M) = +det(R). (C) If M is a matrix with QR-factorization M=QR, then Ris a diagonal matrix if and only if the columns of M are orthogonal to each othe (D) If M is a matrix with QR-factorization M=QR, then QQT = I. (E) Let P be the matrix of the orthogonal projection to a subspace of R". Then P is symmetric. O (A) (B) (C) (D) (E)
Select ALL true statements: (A) For any matrix A, we have det(A" A) > 0. (B) If M is a square matrix with QR-factorization M=QR, then det(M) = +det(R). (C) If M is a matrix with QR-factorization M=QR, then Ris a diagonal matrix if and only if the columns of M are orthogonal to each othe (D) If M is a matrix with QR-factorization M=QR, then QQT = I. (E) Let P be the matrix of the orthogonal projection to a subspace of R". Then P is symmetric. O (A) (B) (C) (D) (E)
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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Transcribed Image Text:Select ALL true statements:
(A) For any matrix A, we have det(A" A) > 0.
(B) If M is a square matrix with QR-factorization M=QR, then det(M) = ±det(R).
(C) If M is a matrix with QR-factorization M=QR, then R is a diagonal matrix if and only if the columns of M are orthogonal to each other.
(D) If M is a matrix with QR-factorization M=QR, then QQT = I.
(E) Let P be the matrix of the orthogonal projection to a subspace of R". Then P is symmetric.
O (A)
O (B)
O (C)
O (D)
O (E)
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