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Recent questions tagged linearalgebra
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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 2021  Question: 38
Let $A$ be a $10\times10$ matrix such that $A^{5}$ is a null matrix, and let $I$ be the $10\times10$ identity matrix. The determinant of $\text{A+I}$ is ___________________.
asked
Feb 20
in
Linear Algebra
by
Arjun
(
7.8k
points)
gateee2021
numericalanswers
linearalgebra
matrices
determinant
0
votes
0
answers
3
GATE Electrical 2020  Question: 42
The number of purely real elements in a lower triangular representation of the given $3\times 3$ ... $5$ $6$ $8$ $9$
asked
Feb 28, 2020
in
Linear Algebra
by
jothee
(
1.8k
points)
gate2020ee
linearalgebra
matrices
0
votes
0
answers
4
Gate2006EE
...
asked
Sep 29, 2019
in
Linear Algebra
by
KUSHAGRA गुप्ता
(
120
points)
gate2006ee
linearalgebra
0
votes
1
answer
5
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
votes
1
answer
6
GATE Electrical 2019  Question: 24
The rank of the matrix, $M = \begin{bmatrix} 0 &1 &1 \\ 1& 0 &1 \\ 1& 1 & 0 \end{bmatrix}$, is ______________.
asked
Feb 12, 2019
in
Linear Algebra
by
Arjun
(
7.8k
points)
gate2019ee
numericalanswers
linearalgebra
matrices
rankofmatrix
0
votes
0
answers
7
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
8
GATE Electrical 2012  Question: 41
The state variable description of an LTI system is given by ... $a_1 = 0, \: a_2 \neq 0, \: a_3 = 0$ $a_1 \neq 0, \: a_2 \neq 0, \: a_3 = 0$
asked
Mar 24, 2018
in
Linear Algebra
by
Andrijana3306
(
1.4k
points)
gate2012ee
linearalgebra
matrices
systemoflinearequations
0
votes
0
answers
9
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
10
GATE Electrical 2018  Question: 44
Let $A= \begin{bmatrix} 1 & 0 & 1 \\ 1 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}$ and $B=A^3A^24A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$ is _______ (up to $1$ decimal place).
asked
Feb 19, 2018
in
Linear Algebra
by
Arjun
(
7.8k
points)
gate2018ee
numericalanswers
linearalgebra
matrices
determinant
0
votes
0
answers
11
GATE Electrical 2018  Question: 17
Consider a nonsingular $2 \times 2$ square matrix $\textbf{A}$. If $\text{trace}(\textbf{A})=4$ and $\text{trace}(\textbf{A}^2)=5$, the determinant of the matrix $\textbf{A}$ is _________ (up to $1$ decimal place).
asked
Feb 19, 2018
in
Linear Algebra
by
Arjun
(
7.8k
points)
gate2018ee
numericalanswers
linearalgebra
matrices
determinant
0
votes
0
answers
12
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
13
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
+1
vote
0
answers
14
GATE Electrical 2013  Question: 50
The state variable formulation of a system is given as ... The system is controllable but not observable not controllable but observable both controllable and observable both not controllable and not observable
asked
Feb 12, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2013ee
linearalgebra
matrices
stateequations
systemoflinearequations
0
votes
0
answers
15
GATE Electrical 2013  Question: 51
The state variable formulation of a system is given as $\begin{bmatrix} x^\cdot_1 \\ x^\cdot_2 \end{bmatrix}=\begin{bmatrix} 2 & 0\\ 0 & 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ , $x_1(0)=0$ , $x_2(0)=0$ ... $1\dfrac{1}{2}e^{2t}\dfrac{1}{2}e^{t} \\$ $e^{2t}e^{t} \\$ $1e^{t}$
asked
Feb 12, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2013ee
linearalgebra
matrices
stateequations
systemoflinearequations
0
votes
0
answers
16
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 $\begin{bmatrix} 1 & 1\\ 1 & 2 \end{bmatrix} \\$ ... $\begin{bmatrix} 0& 1\\ 2 & 3 \end{bmatrix}$
asked
Feb 12, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2013ee
linearalgebra
matrices
eigenvalues
eigenvectors
0
votes
0
answers
17
GATE Electrical 2013  Question: 25
The equation$\begin{bmatrix} 2&2 \\ 1& 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}=\begin{bmatrix} 0\\0 \end{bmatrix}$ has no solution only one solution $\begin{bmatrix} x1\\x2 \end{bmatrix}=\begin{bmatrix} 0\\0 \end{bmatrix}$ nonzero unique solution multiple solutions
asked
Feb 12, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2013ee
linearalgebra
matrices
systemoflinearequations
0
votes
0
answers
18
GATE Electrical 2014 Set 3  Question: 1
Two matrices $A$ and $B$ are given below: $A=\begin{vmatrix} p & q\\ r & s \end{vmatrix}$; $B=\begin{vmatrix} p^2+q^2 & pr+qs\\ pr+qs &r^2+s^2 \end{vmatrix}$ If the rank of matrix $A$ is $N$, then the rank of matrix $B$ is $N/2$ $N – 1$ $N$ $2N$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2014ee3
linearalgebra
matrices
rankofmatrix
0
votes
0
answers
19
GATE Electrical 2014 Set 2  Question: 18
The state transition matrix for the system $\begin{bmatrix} \dot{x_1}\\ \dot{x_2} \end{bmatrix}=\begin{bmatrix} 1 & 0\\ 1 & 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ ... $\begin{bmatrix} e^t &te^t \\ 0&e^t \end{bmatrix}$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2014ee2
linearalgebra
matrices
transitionmatrix
+1
vote
1
answer
20
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
(
9.3k
points)
gate2014ee2
linearalgebra
eigenvalues
0
votes
0
answers
21
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
22
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 ... $P \equiv Q \not\equiv R \equiv S$ $P\not\equiv Q \not\equiv R \not\equiv S$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2015ee2
linearalgebra
systemoflinearequations
eigenvalues
0
votes
0
answers
23
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
votes
0
answers
24
GATE Electrical 2015 Set 1  Question: 3
If the sum of the diagonal elements of a $2 \times 2$ matrix is $6$, then the maximum possible value of determinant of the matrix is ________
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
linearalgebra
matrices
determinant
numericalanswers
0
votes
0
answers
25
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
votes
0
answers
26
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
votes
0
answers
27
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
(
9.3k
points)
gate2016ee2
linearalgebra
matrices
eigenvalues
0
votes
0
answers
28
GATE Electrical 2016 Set 1  Question: 29
Let $A$ be a $4 \times 3$ real matrix with rank $2$. Which one of the following statement is TRUE? Rank of $A^{T} A$ is less than $2$. Rank of $A^{T} A$ is equal to $2$. Rank of $A^{T} A$ is greater than $2$. Rank of $A^{T} A$ can be any number between $1$ and $3$.
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
linearalgebra
matrices
rankofmatrix
0
votes
0
answers
29
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
(
9.3k
points)
gate2016ee1
linearalgebra
matrices
eigenvalues
eigenvectors
0
votes
0
answers
30
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
(
9.3k
points)
gate2016ee1
linearalgebra
matrices
eigenvalues
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