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Recent questions tagged eigenvalues
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1
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 $pq$
asked
Feb 20
in
Linear Algebra
by
Arjun
(
7.8k
points)
gateee2021
linearalgebra
matrices
eigenvalues
0
votes
1
answer
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 $81$
asked
Feb 12, 2019
in
Linear Algebra
by
Arjun
(
7.8k
points)
gate2019ee
linearalgebra
matrices
eigenvalues
0
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0
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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
asked
Feb 12, 2019
in
Linear Algebra
by
Arjun
(
7.8k
points)
gate2019ee
linearalgebra
matrices
eigenvalues
eigenvectors
0
votes
0
answers
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 $15 \: \textbf{A} + 12 \: \textbf{I}$ $19 \: \textbf{A} + 30 \: \textbf{I}$ $17 \: \textbf{A} + 15 \: \textbf{I}$ $17 \: \textbf{A} + 21 \: \textbf{I}$
asked
Mar 24, 2018
in
Linear Algebra
by
Andrijana3306
(
1.4k
points)
gate2012ee
linearalgebra
matrices
eigenvalues
0
votes
0
answers
5
GATE Electrical 2017 Set 2  Question: 28
The eigenvalues of the matrix given below are $\begin{bmatrix} 0 & 1 & 0\\ 0 & 0 & 1\\ 0 & 3 & 4 \end{bmatrix}$ $(0, 1, 3)$ $(0, 2, 3)$ $(0, 2, 3)$ $(0, 1, 3)$
asked
Feb 27, 2017
in
Linear Algebra
by
Arjun
(
7.8k
points)
gate2017ee2
linearalgebra
matrices
eigenvalues
0
votes
0
answers
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 $\begin{bmatrix} 1\\ 0\\ 1 \end{bmatrix}$. ... $\begin{bmatrix} 1\\ 0\\ 1 \end{bmatrix}$ $\begin{bmatrix} 1\\ 1\\ 1 \end{bmatrix}$
asked
Feb 27, 2017
in
Linear Algebra
by
Arjun
(
7.8k
points)
gate2017ee1
linearalgebra
matrices
eigenvalues
eigenvectors
0
votes
0
answers
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 $\begin{bmatrix} 1 & 1\\ 1 & 2 \end{bmatrix} \\$ ... $\begin{bmatrix} 0& 1\\ 2 & 3 \end{bmatrix}$
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Feb 12, 2017
in
Linear Algebra
by
piyag476
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1.5k
points)
gate2013ee
linearalgebra
matrices
eigenvalues
eigenvectors
+1
vote
1
answer
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.
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
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9.3k
points)
gate2014ee2
linearalgebra
eigenvalues
0
votes
0
answers
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 _______
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2014ee1
linearalgebra
matrices
eigenvalues
numericalanswers
0
votes
0
answers
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 are linearly ... $P \equiv Q \not\equiv R \equiv S$ $P\not\equiv Q \not\equiv R \not\equiv S$
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Feb 12, 2017
in
Linear Algebra
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makhdoom ghaya
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9.3k
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gate2015ee2
linearalgebra
systemoflinearequations
eigenvalues
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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 $\dfrac{2}{3\sqrt{3}} \\$ $\dfrac{1}{3\sqrt{3}} \\$ $\dfrac{1+2\sqrt{3}}{3\sqrt{3}} \\$ $\dfrac{1+\sqrt{3}}{3\sqrt{3}}$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
linearalgebra
matrices
eigenvalues
eigenvectors
0
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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 ... $e^{\lambda_{2}t}\alpha$ $e^{\lambda_{1}t}\alpha+e^{\lambda_{2}t}\beta$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
linearalgebra
eigenvalues
eigenvectors
0
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0
answers
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 $\begin{pmatrix} 1\\ 1 \end{pmatrix}$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
linearalgebra
matrices
eigenvalues
eigenvectors
0
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0
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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 $1, 1, −1$ $1, 0.5 + ݆j0.866, 0.5 − ݆j0.866$ $1,−0.5 + ݆j0.866, −0.5 − ݆j0.866$ $0, 1, −1$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
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9.3k
points)
gate2016ee2
linearalgebra
matrices
eigenvalues
0
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0
answers
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 $2, 14; x_{1}, x_{2}$ $2, 14; x_{1}+ x_{2}, x_{1}  x_{2}$ $2, 0; x_{1}, x_{2}$ $2, 0; x_{1}+ x_{2}, x_{1}  x_{2}$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
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9.3k
points)
gate2016ee1
linearalgebra
matrices
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eigenvectors
0
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0
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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 nonzero eigenvalue is ________.
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
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9.3k
points)
gate2016ee1
linearalgebra
matrices
eigenvalues
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