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

Digital Modulation (BPSK, QPSK, QAM, Constellation Diagrams, BER, SNR) question bank (Electromagnetics & Communication Systems)

Practice 7 free GATE & PSUs - Electrical & Electronics Engineering (EE & ECE) Electromagnetics & Communication Systems - Digital Modulation (BPSK, QPSK, QAM, Constellation Diagrams, BER, SNR) questions with answers and step-by-step solutions.

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Q1.
[Digital Modulation (BPSK, QPSK, QAM, Constellation Diagrams, BER, SNR) Concept 5] 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.
[Digital Modulation (BPSK, QPSK, QAM, Constellation Diagrams, BER, SNR) Concept 15] 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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