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Lis Given an ʼn × ʼn matrix A and a nonsingular nxn matrix P all of whose columns are eigenvectors of A. Which of the following statements are always TRUE? Select all that apply. A is nonsingular. has n distinct eigenvalues. AP= PD, for some diagonal matrix D A is diagonalizable. A has ♬ linearly independent eigenvectors.

Lis Given an ʼn × ʼn matrix A and a nonsingular nxn matrix P all of whose columns are eigenvectors of A. Which of the following statements are always TRUE? Select all that apply. A is nonsingular. has n distinct eigenvalues. AP= PD, for some diagonal matrix D A is diagonalizable. A has ♬ linearly independent eigenvectors.

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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Given an ʼn x n matrix A and a nonsingular nxn matrix P all of whose columns are eigenvectors of A. Which of the following statements are always TRUE? Select all that apply. A is nonsingular. has distinct eigenvalues. AP = PD, for some diagonal matrix D x A is diagonalizable. A has linearly independent eigenvectors.
Transcribed Image Text:Given an ʼn x n matrix A and a nonsingular nxn matrix P all of whose columns are eigenvectors of A. Which of the following statements are always TRUE? Select all that apply. A is nonsingular. has distinct eigenvalues. AP = PD, for some diagonal matrix D x A is diagonalizable. A has linearly independent eigenvectors.
Let A be an n x n matrix that has n distinct eigenvalues A₁, A, with corresponding eigenvectors P₁, P₁. Which of the following statements are always TRUE? Select all that apply. PL P are mutually orthogonal. A is diagonalizable. A is nonsingular. P₁, P₁ are linearly independent.
Transcribed Image Text:Let A be an n x n matrix that has n distinct eigenvalues A₁, A, with corresponding eigenvectors P₁, P₁. Which of the following statements are always TRUE? Select all that apply. PL P are mutually orthogonal. A is diagonalizable. A is nonsingular. P₁, P₁ are linearly independent.
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