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.

Since you have asked multiple question, we will solve the first question for you. If youwant any…

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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Question

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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