GATE & PSUs - Electrical & Electronics Engineering (EE & ECE)

Classification of Signals & Systems (Linearity, Causality, Time-Invariance) question bank (Signals & Systems)

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Q1.

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.

[Classification of Signals & Systems (Linearity, Causality, Time-Invariance) Concept 6] A train running at $72\text{ km/h}$ crosses a stationary platform of length $250\text{ m}$ in $26\text{ seconds}$. What is the length of the train?

(A)

$270\text{ m}$

(B)

$200\text{ m}$

(C)

$300\text{ m}$

(D)

$250\text{ m}$

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