(a) Let F = Z5, V = F^2, W = F^3 as vector spaces over Z5 and let T : V → W be defined by T(x, y) = (x + y, y, x + 2y). Find the matrix representation of T and a basis for both KerT, ImmT. b) Let A, B be similar matrices. If λ is an eigenvalue of A with corresponding eigenvector X. Show λ is an eigenvalue of B and find the corresponding eigenvector.
(a) Let F = Z5, V = F^2, W = F^3 as vector spaces over Z5 and let T : V → W be defined by T(x, y) = (x + y, y, x + 2y). Find the matrix representation of T and a basis for both KerT, ImmT. b) Let A, B be similar matrices. If λ is an eigenvalue of A with corresponding eigenvector X. Show λ is an eigenvalue of B and find the corresponding eigenvector.
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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)(a) Let F = Z5, V = F^2, W = F^3
as
by T(x, y) = (x + y, y, x + 2y). Find the matrix representation of T and a basis for both KerT, ImmT.
b) Let A, B be similar matrices. If λ is an eigenvalue of A with corresponding eigenvector X. Show
λ is an eigenvalue of B and find the corresponding eigenvector.
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