Which of the following statements are correct? e) Let A be an n x n matrix. If det(A – \In) = 0 for some A E R, then det(A² – 1²In) 7 0.f) Suppose A is a 3 x 3 matrix having eigenvalues -1, 1, 2. Ak is diagonalizable for any integerk > 0.|1 1 0 02 2 0 0g) The number of linearly independent eigenvectors of the matrixis 3.0 0 2 00 0 0 5h) If A is an eigenvalue of A, then it is also an eigenvalue of A".

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Answered: e) Let A be an n x n matrix. If det(A –…

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e) Let A be an n x n matrix. If det(A – AIn) = 0 for some ) e R, then det(A² – X²In) 70.

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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Question

Which of the following statements are correct?

e) Let A be an n x n matrix. If det(A – \In) = 0 for some A E R, then det(A² – 1²In) 7 0.
f) Suppose A is a 3 x 3 matrix having eigenvalues -1, 1, 2. Ak is diagonalizable for any integer
k > 0.
|
1 1 0 0
2 2 0 0
g) The number of linearly independent eigenvectors of the matrix
is 3.
0 0 2 0
0 0 0 5
h) If A is an eigenvalue of A, then it is also an eigenvalue of A".

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