o. Which of the following statements are true? Select all that apply. D A. IMA is row equivalent to the identity matrix I, then A is diagonalizable. O B. HA is diagonalizable, then the columns of A are linearly independent. O C. 1HA is an nxn diagonalizable matrix, then each vector in R" can be written as a linear combination of eigenvectors of A. O D. If a 5×5 matrix A has fewer than 5 distinct eigenvalues, then A is not diagonalizable. D E. A (square) matrix A is invertible if and only if there is a coordinate system in which the transformation x--Ax is represented by a diagonal matrix.
o. Which of the following statements are true? Select all that apply. D A. IMA is row equivalent to the identity matrix I, then A is diagonalizable. O B. HA is diagonalizable, then the columns of A are linearly independent. O C. 1HA is an nxn diagonalizable matrix, then each vector in R" can be written as a linear combination of eigenvectors of A. O D. If a 5×5 matrix A has fewer than 5 distinct eigenvalues, then A is not diagonalizable. D E. A (square) matrix A is invertible if and only if there is a coordinate system in which the transformation x--Ax is represented by a diagonal matrix.
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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![e. Which of the following statements are true? Select all that apply.
A. IfA is row equivalent to the identity matrix I, then A is diagonalizable.
B. IfA is diagonalizable, then the columns of A are linearly independent.
c. IFA is an nxn diagonalizable matrix, then each vector in R" can be written as a linear combination of eigenvectors of A.
D. If a 5x5 matrix A has fewer than 5 distinct eigenvalues, then A is not diagonalizable.
O E. A (square) matrix A is invertible if and only if there is a coordinate system in which the transformation x--Ax is represented by a diagonal matrix.
1. Which of the following statements are true? Select all that apply.
| A. There exists a 2×2 matrix that has no eigenvectors in R2.
] B. If each vector e in the standard basis for R" is an eigenvector of A, then A is a diagonal matrix.
OC. An nxn matrix with n linearly independent eigenvectors is invertible.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffba142dd-1494-4b78-9e41-2122df5fca48%2F4566fca1-e629-4ebb-b77c-8f69e612be19%2Fw1771e8_processed.png&w=3840&q=75)
Transcribed Image Text:e. Which of the following statements are true? Select all that apply.
A. IfA is row equivalent to the identity matrix I, then A is diagonalizable.
B. IfA is diagonalizable, then the columns of A are linearly independent.
c. IFA is an nxn diagonalizable matrix, then each vector in R" can be written as a linear combination of eigenvectors of A.
D. If a 5x5 matrix A has fewer than 5 distinct eigenvalues, then A is not diagonalizable.
O E. A (square) matrix A is invertible if and only if there is a coordinate system in which the transformation x--Ax is represented by a diagonal matrix.
1. Which of the following statements are true? Select all that apply.
| A. There exists a 2×2 matrix that has no eigenvectors in R2.
] B. If each vector e in the standard basis for R" is an eigenvector of A, then A is a diagonal matrix.
OC. An nxn matrix with n linearly independent eigenvectors is invertible.
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