Suppose A and B have the same eigenvalues A₁,..., An with the same independent=B. Reason: Any vector x is a combinationeigenvectors 1,...,n. Then AC₁1++Cnn. What is Ax? What is Bx?

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Answered: Suppose A and B have the same…

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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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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Suppose A and B have the same eigenvalues A₁,..., An with the same independent eigenvectors ₁,...,n. Then A = B. Reason: Any vector x is a combination C₁1++Cnn. What is Ax? What is Ba?