Recent questions tagged eigen-values / GO Electrical

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GATE Electrical 2021 | Question: 1
Let $p$ and $q$ be real numbers such that $p^{2}+q^{2}=1$ . The eigenvalues of the matrix $\begin{bmatrix} p & q\\ q& -p \end{bmatrix}$are $1$ and $1$ $1$ and $-1$ $j$ and $-j$ $pq$ and $-pq$

Let $p$ and $q$ be real numbers such that $p^{2}+q^{2}=1$ . The eigenvalues of the matrix $\begin{bmatrix} p & q\\ q& -p \end{bmatrix}$are$1$ and $1$$1$ and $-1$$j$ and $...

Arjun

15.9k points

Arjun asked Feb 19, 2021

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2

GATE Electrical 2019 | Question: 2
$M$ is $2 \times 2$ matrix with eigenvalues $4$ and $9.$ The eigenvalues of $M^{2}$ are $4$ and $9$ $2$ and $3$ $-2$ and $-3$ $16$ and $81$

$M$ is $2 \times 2$ matrix with eigenvalues $4$ and $9.$ The eigenvalues of $M^{2}$ are$4$ and $9$$2$ and $3$$-2$ and $-3$$16$ and $81$

Arjun

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Arjun asked Feb 12, 2019

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3

GATE Electrical 2019 | Question: 26
Consider a $2\times 2$ matrix $M=\begin{bmatrix} v_1 & v_2 \end{bmatrix}$, where $v_1$ and $v_2$ are the column vectors. Suppose $M^{-1}=\begin{bmatrix} u_1^T \\ u_2^T \end{bmatrix}$, where $u_1^T$ and $u_2^T$ are ... True and Statement $2$ is false Statement $2$ is true and Statement $1$ is false Both the Statements are true Both the statements are false

Consider a $2\times 2$ matrix $M=\begin{bmatrix} v_1 & v_2 \end{bmatrix}$, where $v_1$ and $v_2$ are the column vectors. Suppose $M^{-1}=\begin{bmatrix} u_1^T \\ u_2^T \e...

Arjun

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Arjun asked Feb 12, 2019

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4

GATE Electrical 2012 | Question: 26
Given that $\textbf{A}= \begin{bmatrix} -5 & -3 \\ 2 & 0 \end{bmatrix}$ and $\textbf{I} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, the value of $A^3$ is $15 \: \textbf{A} + 12 \: \textbf{I}$ $19 \: \textbf{A} + 30 \: \textbf{I}$ $17 \: \textbf{A} + 15 \: \textbf{I}$ $17 \: \textbf{A} + 21 \: \textbf{I}$

Given that $\textbf{A}= \begin{bmatrix} -5 & -3 \\ 2 & 0 \end{bmatrix}$ and $\textbf{I} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, the value of $A^3$ is$15 \: \text...

Andrijana3306

1.4k points

Andrijana3306 asked Mar 23, 2018

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5

GATE Electrical 2017 Set 2 | Question: 28
The eigenvalues of the matrix given below are $\begin{bmatrix} 0 & 1 & 0\\ 0 & 0 & 1\\ 0 & -3 & -4 \end{bmatrix}$ $(0, -1, -3)$ $(0, -2, -3)$ $(0, 2, 3)$ $(0, 1, 3)$

The eigenvalues of the matrix given below are$\begin{bmatrix}0 & 1 & 0\\ 0 & 0 & 1\\ 0 & -3 & -4\end{bmatrix}$$(0, -1, -3)$$(0, -2, -3)$$(0, 2, 3)$$(0, 1, 3)$

Arjun

15.9k points

Arjun asked Feb 26, 2017

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6

GATE Electrical 2017 Set 1 | Question: 1
The matrix $A=\begin{bmatrix} \frac{3}{2} &0 & \frac{1}{2}\\ 0& -1 &0 \\ \frac{1}{2} & 0 & \frac{3}{2} \end{bmatrix}$ has three distinct eigenvalues and one of its eigenvectors is $\begin{bmatrix} 1\\ 0\\ 1 \end{bmatrix}$. ... $\begin{bmatrix} 1\\ 0\\ -1 \end{bmatrix}$ $\begin{bmatrix} 1\\ -1\\ 1 \end{bmatrix}$

The matrix $A=\begin{bmatrix}\frac{3}{2} &0 & \frac{1}{2}\\ 0& -1 &0 \\ \frac{1}{2} & 0 & \frac{3}{2}\end{bmatrix}$ has three distinct eigenvalues and one of its eigenv...

Arjun

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Arjun asked Feb 26, 2017

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7

GATE Electrical 2013 | Question: 35
A matrix has eigenvalues $-1$ and $-2$. The corresponding eigenvectors are $\begin{bmatrix} 1\\-1 \end{bmatrix}$ and $\begin{bmatrix} 1\\-2 \end{bmatrix}$ respectibely. The matrix is $\begin{bmatrix} 1 & 1\\ -1 & -2 \end{bmatrix} \\$ ... $\begin{bmatrix} 0& 1\\ -2 & 3 \end{bmatrix}$

A matrix has eigenvalues $–1$ and $–2$. The corresponding eigenvectors are $\begin{bmatrix} 1\\-1 \end{bmatrix}$ and $\begin{bmatrix} 1\\-2 \end{bmatrix}$ respectibel...

piyag476

1.6k points

piyag476 asked Feb 11, 2017

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8

GATE Electrical 2014 Set 2 | Question: 1
Which one of the following statements is true for all real symmetric matrices? All the eigenvalues are real. All the eigenvalues are positive. All the eigenvalues are distinct. Sum of all the eigenvalues is zero.

Which one of the following statements is true for all real symmetric matrices?All the eigenvalues are real.All the eigenvalues are positive.All the eigenvalues are distin...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Feb 11, 2017

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9

GATE Electrical 2014 Set 1 | Question: 46
A system matrix is given as follows. $A=\begin{bmatrix} 0 & 1 & -1\\ -6 & -11 &6 \\ -6& -11& 5 \end{bmatrix}$ The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is _______

A system matrix is given as follows.$A=\begin{bmatrix} 0 & 1 & -1\\ -6 & -11 &6 \\ -6& -11& 5 \end{bmatrix}$The absolute value of the ratio of the maximum eigenvalue to t...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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10

GATE Electrical 2015 Set 2 | Question: 2
We have a set of $3$ linear equations in $3$ unknowns. $'X \equiv Y'$ means $X$ and $Y$ are equivalent statements and $'X \not\equiv Y'$ means $X$ and $Y$ are not equivalent statements. P: There is a unique solution. Q: The equations ... $P \equiv Q \not\equiv R \equiv S$ $P\not\equiv Q \not\equiv R \not\equiv S$

We have a set of $3$ linear equations in $3$ unknowns. $'X \equiv Y'$ means $X$ and $Y$ are equivalent statements and $'X \not\equiv Y'$ means $X$ and $Y$ are not equiva...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Feb 11, 2017

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11

GATE Electrical 2015 Set 1 | Question: 26
The maximum value of "a" such that the matrix $\begin{pmatrix} -3&0&-2 \\ 1&-1&0 \\ 0&a&-2 \end{pmatrix}$ has three linearly independent real eigenvectors is $\dfrac{2}{3\sqrt{3}} \\$ $\dfrac{1}{3\sqrt{3}} \\$ $\dfrac{1+2\sqrt{3}}{3\sqrt{3}} \\$ $\dfrac{1+\sqrt{3}}{3\sqrt{3}}$

The maximum value of "a" such that the matrix $\begin{pmatrix} -3&0&-2 \\ 1&-1&0 \\ 0&a&-2 \end{pmatrix}$ has three linearly independent real eigenvectors is$\dfrac{2}{...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Feb 11, 2017

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12

GATE Electrical 2016 Set 2 | Question: 49
Consider a linear time invariant system $\dot{x}=Ax$ with initial condition $x(0)$ at $t=0$. Suppose $\alpha$ and $\beta$ are eigenvectors of $(2 \times 2)$ matrix $A$ corresponding to distinct eigenvalues $\lambda_{1}$ and $\lambda_{2}$ respectively. Then the ... $e^{\lambda_{2}t}\alpha$ $e^{\lambda_{1}t}\alpha+e^{\lambda_{2}t}\beta$

Consider a linear time invariant system $\dot{x}=Ax$ with initial condition $x(0)$ at $t=0$. Suppose $\alpha$ and $\beta$ are eigenvectors of $(2 \times 2)$ matrix $A$ co...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Jan 29, 2017

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13

GATE Electrical 2016 Set 2 | Question: 32
Let $P=\begin{bmatrix} 3&1 \\ 1 & 3 \end{bmatrix}$ Consider the set $S$ of all vectors $\begin{pmatrix} x\\ y \end{pmatrix}$ such that $a^{2}+b^{2}=1$ ... with major axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$ An ellipse with minor axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$

Let $P=\begin{bmatrix} 3&1 \\ 1 & 3\end{bmatrix}$ Consider the set $S$ of all vectors $\begin{pmatrix}x\\ y\end{pmatrix}$ such that $a^{2}+b^{2}=1$ where $\begin{pmatrix}...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Jan 29, 2017

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14

GATE Electrical 2016 Set 2 | Question: 7
A $3 \times 3$ matrix $P$ is such that, $P^{3}=P$. Then the eigenvalues of $P$ ܲ are $1, 1, −1$ $1, 0.5 + ݆j0.866, 0.5 − ݆j0.866$ $1,−0.5 + ݆j0.866, −0.5 − ݆j0.866$ $0, 1, −1$

A $3 \times 3$ matrix $P$ is such that, $P^{3}=P$. Then the eigenvalues of $P$ ܲ are$1, 1, −1$$1, 0.5 + ݆j0.866, 0.5 − ݆j0.866$ $1,−0.5 + ݆j0.866, −0.5 − ݆...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Jan 29, 2017

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15

GATE Electrical 2016 Set 1 | Question: 28
Let the eigenvalues of a $2 \times 2$ matrix $A$ be $1, -2$ with eigenvectors $x_{1}$ and $x_{2}$ respectively. Then the eigenvalues and eigenvectors of the matrix $A^{2}-3A+4I$ would, respectively, be $2, 14; x_{1}, x_{2}$ $2, 14; x_{1}+ x_{2}, x_{1} - x_{2}$ $2, 0; x_{1}, x_{2}$ $2, 0; x_{1}+ x_{2}, x_{1} - x_{2}$

Let the eigenvalues of a $2 \times 2$ matrix $A$ be $1, -2$ with eigenvectors $x_{1}$ and $x_{2}$ respectively. Then the eigenvalues and eigenvectors of the matrix $A^{2}...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Jan 29, 2017

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16

GATE Electrical 2016 Set 1 | Question: 2
Consider a $3 \times 3$ matrix with every element being equal to $1$. Its only non-zero eigenvalue is ________.

Consider a $3 \times 3$ matrix with every element being equal to $1$. Its only non-zero eigenvalue is ________.

makhdoom ghaya

9.4k points

makhdoom ghaya asked Jan 29, 2017