Please solve the question of a,b,c,d options. 3 4 825. Is the vector a =1an eigenvector of the matrix A =2 142 2 3(a) Find the characteristic polynomial A4(X) of A. (If you cannot findit, assume that A4(X) = X³ - 7X2- 17X - 9 = (X-9) (X+1)and go on.)|| (b) What are the eigenvalues of A and also det A?(c) If A is diagonalizable find a diagonalizing matrix for A.(d) If A is invertible write A as a linear combination of the matricesI. A and A226. The following veetors(1.0.1.2)(3.0,9.3)

Answered: Image /qna-images/answer/65ddc89d-5205-4c0e-a035-17e83f0556cb.jpg

3 4 8 2 1 4 2 2 3 25. Is the vector a = an eigenvector of the matrix A = (a) Find the characteristic polynomial AA(X) of A. (If you cannot find it, assume that A4(X) = X³ – 7X2- 17X-9 3 (X- 9) (X +1) and go on.)

3 4 8 2 1 4 2 2 3 25. Is the vector a = an eigenvector of the matrix A = (a) Find the characteristic polynomial AA(X) of A. (If you cannot find it, assume that A4(X) = X³ – 7X2- 17X-9 3 (X- 9) (X +1) and go on.)

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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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

Please solve the question of a,b,c,d options.

3 4 8
25. Is the vector a =
1
an eigenvector of the matrix A =
2 1
4
2 2 3
(a) Find the characteristic polynomial A4(X) of A. (If you cannot find
it, assume that A4(X) = X³ - 7X2- 17X - 9 = (X-9) (X+1)
and go on.)
||

(b) What are the eigenvalues of A and also det A?
(c) If A is diagonalizable find a diagonalizing matrix for A.
(d) If A is invertible write A as a linear combination of the matrices
I. A and A2
26. The following veetors
(1.0.1.2)
(3.0,9.3)

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