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If A and B are n x n matrices, and I is the n x n identity matrix. Which of the following is/are true? (Select all that apply) If A is an eigenvalue of A, then the matrix A-XI is invertible. □ If A is an eigenvalue of A, then (A-XI)x= 0 has a nontrivial solution. The eigenspace of A corresponding to an eigenvalue A is the column space of A - XI. If x is an eigenvector of both A and B, then x is also an eigenvector of A+B. If A is an eigenvalue of both A and B, then A is also an eigenvalue of A+B.

If A and B are n x n matrices, and I is the n x n identity matrix. Which of the following is/are true? (Select all that apply) If A is an eigenvalue of A, then the matrix A-XI is invertible. □ If A is an eigenvalue of A, then (A-XI)x= 0 has a nontrivial solution. The eigenspace of A corresponding to an eigenvalue A is the column space of A - XI. If x is an eigenvector of both A and B, then x is also an eigenvector of A+B. If A is an eigenvalue of both A and B, then A is also an eigenvalue of A+B.

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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If A and B are n x n matrices, and I is the n x n identity matrix. Which of the following is/are true? (Select all that apply) If A is an eigenvalue of A, then the matrix A-XI is invertible. □ If A is an eigenvalue of A, then (A-XI)x= 0 has a nontrivial solution. The eigenspace of A corresponding to an eigenvalue A is the column space of A - XI. If x is an eigenvector of both A and B, then x is also an eigenvector of A+B. If A is an eigenvalue of both A and B, then A is also an eigenvalue of A+B.
Transcribed Image Text:If A and B are n x n matrices, and I is the n x n identity matrix. Which of the following is/are true? (Select all that apply) If A is an eigenvalue of A, then the matrix A-XI is invertible. □ If A is an eigenvalue of A, then (A-XI)x= 0 has a nontrivial solution. The eigenspace of A corresponding to an eigenvalue A is the column space of A - XI. If x is an eigenvector of both A and B, then x is also an eigenvector of A+B. If A is an eigenvalue of both A and B, then A is also an eigenvalue of A+B.
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