(d) If v is an eigenvector for a matrix A and a matrix B then v is an eigenvector for A+ B.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...
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please answer PART D

Mark as TRUE or FALSE. You will need to give an explanation.
(a) If v1, v2 ..., Vn are linearly independent, then v1, V2 are linearly independent.
(b) If v and w are two eigenvectors for the same eigenvalue c, then the sum v + w is also an
eigenvector for the eigenvalue c.
(c) Any 2 x 2 matrix has a real eigenvalue.
(d) If v is an eigenvector for a matrix A and a matrix B then v is an eigenvector for A+ B.
Transcribed Image Text:Mark as TRUE or FALSE. You will need to give an explanation. (a) If v1, v2 ..., Vn are linearly independent, then v1, V2 are linearly independent. (b) If v and w are two eigenvectors for the same eigenvalue c, then the sum v + w is also an eigenvector for the eigenvalue c. (c) Any 2 x 2 matrix has a real eigenvalue. (d) If v is an eigenvector for a matrix A and a matrix B then v is an eigenvector for A+ B.
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