GATE & PSUs - Engineering Mathematics & General Aptitude (Common)

Eigenvalues & Eigenvectors (Cayley-Hamilton Theorem) question bank (Linear Algebra)

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Q1.

[Eigenvalues & Eigenvectors (Cayley-Hamilton Theorem) Concept 3] The matrix $A = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}$ has eigenvalues $\lambda_1$ and $\lambda_2$. What are the eigenvalues of the matrix $A^3 - 2A + I$?

(A)

$22$ and $0$

(B)

$8$ and $1$

(C)

$27$ and $1$

(D)

$24$ and $2$

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Q2.

[Eigenvalues & Eigenvectors (Cayley-Hamilton Theorem) Concept 7] The matrix $A = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}$ has eigenvalues $\lambda_1$ and $\lambda_2$. What are the eigenvalues of the matrix $A^3 - 2A + I$?

(A)

$22$ and $0$

(B)

$8$ and $1$

(C)

$27$ and $1$

(D)

$24$ and $2$

Show answer & solution

Verified Answer & Solution Locked

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