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Recent questions tagged eigen-values
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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 $-pq$
Arjun
asked
in
Linear Algebra
Feb 20, 2021
by
Arjun
9.3k
points
gateee-2021
linear-algebra
matrices
eigen-values
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 $81$
Arjun
asked
in
Linear Algebra
Feb 12, 2019
by
Arjun
9.3k
points
gate2019-ee
linear-algebra
matrices
eigen-values
0
votes
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
Arjun
asked
in
Linear Algebra
Feb 12, 2019
by
Arjun
9.3k
points
gate2019-ee
linear-algebra
matrices
eigen-values
eigen-vectors
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 $15 \: \textbf{A} + 12 \: \textbf{I}$ $19 \: \textbf{A} + 30 \: \textbf{I}$ $17 \: \textbf{A} + 15 \: \textbf{I}$ $17 \: \textbf{A} + 21 \: \textbf{I}$
Andrijana3306
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in
Linear Algebra
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
linear-algebra
matrices
eigen-values
0
votes
0
answers
5
GATE Electrical 2017 Set 2 | Question: 28
The eigenvalues of the matrix given below are $\begin{bmatrix} 0 & 1 & 0\\ 0 & 0 & 1\\ 0 & -3 & -4 \end{bmatrix}$ $(0, -1, -3)$ $(0, -2, -3)$ $(0, 2, 3)$ $(0, 1, 3)$
Arjun
asked
in
Linear Algebra
Feb 27, 2017
by
Arjun
9.3k
points
gate2017-ee-2
linear-algebra
matrices
eigen-values
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 $\begin{bmatrix} 1\\ 0\\ 1 \end{bmatrix}$. ... $\begin{bmatrix} 1\\ 0\\ -1 \end{bmatrix}$ $\begin{bmatrix} 1\\ -1\\ 1 \end{bmatrix}$
Arjun
asked
in
Linear Algebra
Feb 27, 2017
by
Arjun
9.3k
points
gate2017-ee-1
linear-algebra
matrices
eigen-values
eigen-vectors
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 $\begin{bmatrix} 1 & 1\\ -1 & -2 \end{bmatrix} \\$ ... $\begin{bmatrix} 0& 1\\ -2 & 3 \end{bmatrix}$
piyag476
asked
in
Linear Algebra
Feb 12, 2017
by
piyag476
1.5k
points
gate2013-ee
linear-algebra
matrices
eigen-values
eigen-vectors
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.
makhdoom ghaya
asked
in
Linear Algebra
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-2
linear-algebra
eigen-values
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 _______
makhdoom ghaya
asked
in
Linear Algebra
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-1
linear-algebra
matrices
eigen-values
numerical-answers
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 ... $P \equiv Q \not\equiv R \equiv S$ $P\not\equiv Q \not\equiv R \not\equiv S$
makhdoom ghaya
asked
in
Linear Algebra
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2015-ee-2
linear-algebra
system-of-linear-equations
eigen-values
0
votes
0
answers
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 $\dfrac{2}{3\sqrt{3}} \\$ $\dfrac{1}{3\sqrt{3}} \\$ $\dfrac{1+2\sqrt{3}}{3\sqrt{3}} \\$ $\dfrac{1+\sqrt{3}}{3\sqrt{3}}$
makhdoom ghaya
asked
in
Linear Algebra
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2015-ee-1
linear-algebra
matrices
eigen-values
eigen-vectors
0
votes
0
answers
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 ... $e^{\lambda_{2}t}\alpha$ $e^{\lambda_{1}t}\alpha+e^{\lambda_{2}t}\beta$
makhdoom ghaya
asked
in
Linear Algebra
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-2
linear-algebra
eigen-values
eigen-vectors
0
votes
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 $\begin{pmatrix} 1\\ 1 \end{pmatrix}$
makhdoom ghaya
asked
in
Linear Algebra
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-2
linear-algebra
matrices
eigen-values
eigen-vectors
0
votes
0
answers
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 $1, 1, −1$ $1, 0.5 + ݆j0.866, 0.5 − ݆j0.866$ $1,−0.5 + ݆j0.866, −0.5 − ݆j0.866$ $0, 1, −1$
makhdoom ghaya
asked
in
Linear Algebra
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-2
linear-algebra
matrices
eigen-values
0
votes
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 $2, 14; x_{1}, x_{2}$ $2, 14; x_{1}+ x_{2}, x_{1} - x_{2}$ $2, 0; x_{1}, x_{2}$ $2, 0; x_{1}+ x_{2}, x_{1} - x_{2}$
makhdoom ghaya
asked
in
Linear Algebra
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-1
linear-algebra
matrices
eigen-values
eigen-vectors
0
votes
0
answers
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 ________.
makhdoom ghaya
asked
in
Linear Algebra
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-1
linear-algebra
matrices
eigen-values
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