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Which of the following are true? (Select all that apply) □ If A is a real symmetric matrix then A is diagonalizable by means of an orthogonal matrix. A matrix A is positive definite if all of its eigenvalues are positive. □ If A is a real n x n symmetric square matrix then there exists a set of n orthonormal eigenvectors. ✔ A positive definite matrix is invertible.

Which of the following are true? (Select all that apply) □ If A is a real symmetric matrix then A is diagonalizable by means of an orthogonal matrix. A matrix A is positive definite if all of its eigenvalues are positive. □ If A is a real n x n symmetric square matrix then there exists a set of n orthonormal eigenvectors. ✔ A positive definite matrix is invertible.

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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The two that are checked are true for sure, but I can't find where the textbook mentions anything about the others. Thank you.

Which of the following are true? (Select all that apply) □ If A is a real symmetric matrix then A is diagonalizable by means of an orthogonal matrix. A matrix A is positive definite if all of its eigenvalues are positive. □ If A is a real n x n symmetric square matrix then there exists a set of n orthonormal eigenvectors. A positive definite matrix is invertible. ✓ The eigenvalues of a skew-symmetric matrix are 0 or pure imaginary.
Transcribed Image Text:Which of the following are true? (Select all that apply) □ If A is a real symmetric matrix then A is diagonalizable by means of an orthogonal matrix. A matrix A is positive definite if all of its eigenvalues are positive. □ If A is a real n x n symmetric square matrix then there exists a set of n orthonormal eigenvectors. A positive definite matrix is invertible. ✓ The eigenvalues of a skew-symmetric matrix are 0 or pure imaginary.
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