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Recent questions and answers in Linear Algebra
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1
GATE Electrical 2020 | Question: 42
The number of purely real elements in a lower triangular representation of the given $3\times 3$ ... $5$ $6$ $8$ $9$
samarpita
answered
in
Linear Algebra
May 7
by
samarpita
140
points
gate2020-ee
linear-algebra
matrices
0
votes
1
answer
2
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 $-pq$
shreekant98
answered
in
Linear Algebra
Mar 17, 2021
by
shreekant98
280
points
gateee-2021
linear-algebra
matrices
eigen-values
0
votes
1
answer
3
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 ___________________.
shreekant98
answered
in
Linear Algebra
Mar 17, 2021
by
shreekant98
280
points
gateee-2021
numerical-answers
linear-algebra
matrices
determinant
0
votes
0
answers
4
Gate2006-EE
...
KUSHAGRA गुप्ता
asked
in
Linear Algebra
Sep 29, 2019
by
KUSHAGRA गुप्ता
120
points
gate2006-ee
linear-algebra
0
votes
1
answer
5
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 ______________.
Shalini26
answered
in
Linear Algebra
May 29, 2019
by
Shalini26
520
points
gate2019-ee
numerical-answers
linear-algebra
matrices
rank-of-matrix
0
votes
1
answer
6
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 $81$
Shalini26
answered
in
Linear Algebra
May 29, 2019
by
Shalini26
520
points
gate2019-ee
linear-algebra
matrices
eigen-values
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
Arjun
asked
in
Linear Algebra
Feb 12, 2019
by
Arjun
9.2k
points
gate2019-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.
Abhisek Tiwari 4
answered
in
Linear Algebra
Oct 26, 2018
by
Abhisek Tiwari 4
140
points
gate2014-ee-2
linear-algebra
eigen-values
0
votes
0
answers
9
GATE Electrical 2012 | Question: 41
The state variable description of an LTI system is given by ... $a_1 = 0, \: a_2 \neq 0, \: a_3 = 0$ $a_1 \neq 0, \: a_2 \neq 0, \: a_3 = 0$
Andrijana3306
asked
in
Linear Algebra
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
linear-algebra
matrices
system-of-linear-equations
0
votes
0
answers
10
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
11
GATE Electrical 2018 | Question: 44
Let $A= \begin{bmatrix} 1 & 0 & -1 \\ -1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B=A^3-A^2-4A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$ is _______ (up to $1$ decimal place).
Arjun
asked
in
Linear Algebra
Feb 19, 2018
by
Arjun
9.2k
points
gate2018-ee
numerical-answers
linear-algebra
matrices
determinant
0
votes
0
answers
12
GATE Electrical 2018 | Question: 17
Consider a non-singular $2 \times 2$ 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).
Arjun
asked
in
Linear Algebra
Feb 19, 2018
by
Arjun
9.2k
points
gate2018-ee
numerical-answers
linear-algebra
matrices
determinant
0
votes
0
answers
13
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
9.2k
points
gate2017-ee-2
linear-algebra
matrices
eigen-values
0
votes
0
answers
14
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
9.2k
points
gate2017-ee-1
linear-algebra
matrices
eigen-values
eigen-vectors
0
votes
0
answers
15
GATE Electrical 2013 | Question: 51
The state variable formulation of a system is given as $\begin{bmatrix} x^\cdot_1 \\ x^\cdot_2 \end{bmatrix}=\begin{bmatrix} -2 & 0\\ 0 & -1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ , $x_1(0)=0$ , $x_2(0)=0$ ... $1-\dfrac{1}{2}e^{-2t}-\dfrac{1}{2}e^{-t} \\$ $e^{-2t}-e^{-t} \\$ $1-e^{-t}$
piyag476
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in
Linear Algebra
Feb 12, 2017
by
piyag476
1.5k
points
gate2013-ee
linear-algebra
matrices
state-equations
system-of-linear-equations
1
vote
0
answers
16
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
piyag476
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in
Linear Algebra
Feb 12, 2017
by
piyag476
1.5k
points
gate2013-ee
linear-algebra
matrices
state-equations
system-of-linear-equations
0
votes
0
answers
17
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
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gate2013-ee
linear-algebra
matrices
eigen-values
eigen-vectors
0
votes
0
answers
18
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 $\begin{bmatrix} x1\\x2 \end{bmatrix}=\begin{bmatrix} 0\\0 \end{bmatrix}$ non-zero unique solution multiple solutions
piyag476
asked
in
Linear Algebra
Feb 12, 2017
by
piyag476
1.5k
points
gate2013-ee
linear-algebra
matrices
system-of-linear-equations
0
votes
0
answers
19
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 $N/2$ $N – 1$ $N$ $2N$
makhdoom ghaya
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in
Linear Algebra
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-3
linear-algebra
matrices
rank-of-matrix
0
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0
answers
20
GATE Electrical 2014 Set 2 | Question: 18
The state transition matrix for the system $\begin{bmatrix} \dot{x_1}\\ \dot{x_2} \end{bmatrix}=\begin{bmatrix} 1 & 0\\ 1 & 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ ... $\begin{bmatrix} e^t &te^t \\ 0&e^t \end{bmatrix}$
makhdoom ghaya
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in
Linear Algebra
Feb 12, 2017
by
makhdoom ghaya
9.3k
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gate2014-ee-2
linear-algebra
matrices
transition-matrix
0
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0
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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 _______
makhdoom ghaya
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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
22
GATE Electrical 2014 Set 1 | Question: 1
Given a system of equations: $x+2y+2z=b_1$ $5x+y+3z=b_2$ Which of the following is true regarding its solutions The system has a unique solution for any given $b_1$ and $b_2$ The system will have infinitely many solutions for any given $b_1$ ... exists depends on the given $b_1$ and $b_2$ The system would have no solution for any values of $b_1$ and $b_2$
makhdoom ghaya
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in
Linear Algebra
Feb 12, 2017
by
makhdoom ghaya
9.3k
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gate2014-ee-1
linear-equation
system-of-linear-equations
0
votes
0
answers
23
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
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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
24
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
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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
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 ... $e^{\lambda_{2}t}\alpha$ $e^{\lambda_{1}t}\alpha+e^{\lambda_{2}t}\beta$
makhdoom ghaya
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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
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 $\begin{pmatrix} 1\\ 1 \end{pmatrix}$
makhdoom ghaya
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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
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 $1, 1, −1$ $1, 0.5 + ݆j0.866, 0.5 − ݆j0.866$ $1,−0.5 + ݆j0.866, −0.5 − ݆j0.866$ $0, 1, −1$
makhdoom ghaya
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in
Linear Algebra
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-2
linear-algebra
matrices
eigen-values
0
votes
0
answers
28
GATE Electrical 2016 Set 1 | GA Question: 5
In a quadratic function, the value of the product of the roots $(\alpha, \beta)$ is $4$. Find the value of $\dfrac{\alpha^{n}+\beta^{n}}{\alpha^{-n}+\beta^{-n}}$ $n^{4}$ $4^{n}$ $2^{2n-1}$ $4^{n-1}$
makhdoom ghaya
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Linear Algebra
Jan 30, 2017
by
makhdoom ghaya
9.3k
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gate2016-ee-1
functions
roots
sequence
0
votes
0
answers
29
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 $3$.
makhdoom ghaya
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Linear Algebra
Jan 30, 2017
by
makhdoom ghaya
9.3k
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gate2016-ee-1
linear-algebra
matrices
rank-of-matrix
0
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0
answers
30
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
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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
31
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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