2. Let A be a 3 x 3 matrix. Assume 1 and 2 are the only eigenvalues of A. Determine whether the following statements are always true. If true, justify why. If not true, provide a counterexample. Statement A: If v₁ is an eigenvector of A corresponding to 1 and v₂ is an eigenvector corresponding to 2, then A(v₁ + V₂) = 3(V1 + V₂) Statement B: One of the eigenspaces of A is two-dimensional, and the other is one- dimensional.
2. Let A be a 3 x 3 matrix. Assume 1 and 2 are the only eigenvalues of A. Determine whether the following statements are always true. If true, justify why. If not true, provide a counterexample. Statement A: If v₁ is an eigenvector of A corresponding to 1 and v₂ is an eigenvector corresponding to 2, then A(v₁ + V₂) = 3(V1 + V₂) Statement B: One of the eigenspaces of A is two-dimensional, and the other is one- dimensional.
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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just answered q2 pls
Transcribed Image Text:1-
ت ا ا ا ا
1. Find a matrix A with 25 as an eigenvalue with eigenvector V₁
and 0 as an eigenvalue
with eigenvector V2 =
H
Is your matrix invertible? Is it orthogonally diagonalisable?
2. Let A be a 3 x 3 matrix. Assume 1 and 2 are the only eigenvalues of A.
Determine whether the following statements are always true. If true, justify why. If not
true, provide a counterexample.
Statement A: If v₁ is an eigenvector of A corresponding to 1 and v₂ is an eigenvector
corresponding to 2, then A(v₁ + V₂) = 3(V1 + V2)
Statement B: One of the eigenspaces of A is two-dimensional, and the other is one-
dimensional.
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