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Mark only correct statements. a. If u and v are eigenvectors from distinct eigenspaces of a symmetric matrix with real entries, then ||u+v||2||u||2+ ||v||² b. If A is both invertible and orthogonally diagonalizable, then A¹ is orthogonally diagonalizable. □ c. If A is an n x n orthogonally diagonalizable matrix, then there exists an orthonormal basis for R" consisting of eigenvectors of A.

Mark only correct statements. a. If u and v are eigenvectors from distinct eigenspaces of a symmetric matrix with real entries, then ||u+v||2||u||2+ ||v||² b. If A is both invertible and orthogonally diagonalizable, then A¹ is orthogonally diagonalizable. □ c. If A is an n x n orthogonally diagonalizable matrix, then there exists an orthonormal basis for R" consisting of eigenvectors of A.

Advanced Engineering Mathematics
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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please list only correct statements. try to solve this problem as fast as possible please! thank you!

Mark only correct statements. □ a. If u and v are eigenvectors from distinct eigenspaces of a symmetric matrix with real entries, then ||u+v||² = ||u||² + ||v||² Ob. If A is both invertible and orthogonally diagonalizable, then A¹ is orthogonally diagonalizable. O c. If A is an n x n orthogonally diagonalizable matrix, then there exists an orthonormal basis for R" consisting of eigenvectors of A. Od. If \(\mathbf {A}) is orthogonally diagonalizable, then \(\mathbf {A}) has real eigenvalues. e. If A is a square matrix, then ATA and AAT are orthogonally diagonalizable. f. Every orthogonal matrix is orthogonally diagonalizable. g. Every eigenvalue of an orthogonal matrix has absolute value 1. n
Transcribed Image Text:Mark only correct statements. □ a. If u and v are eigenvectors from distinct eigenspaces of a symmetric matrix with real entries, then ||u+v||² = ||u||² + ||v||² Ob. If A is both invertible and orthogonally diagonalizable, then A¹ is orthogonally diagonalizable. O c. If A is an n x n orthogonally diagonalizable matrix, then there exists an orthonormal basis for R" consisting of eigenvectors of A. Od. If \(\mathbf {A}) is orthogonally diagonalizable, then \(\mathbf {A}) has real eigenvalues. e. If A is a square matrix, then ATA and AAT are orthogonally diagonalizable. f. Every orthogonal matrix is orthogonally diagonalizable. g. Every eigenvalue of an orthogonal matrix has absolute value 1. n
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