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Recent questions and answers in Linear Algebra
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GATE BT 2021 | Question: 44
The determinant of matrix $A = \begin{pmatrix} 1 & 1& 1 & 1 \\ -1 & 1 & 1 & 1 \\ -1 & -1 & 1 & 1 \\ 1 & 1 & 1 & 3 \end{pmatrix}$ is __________.
go_editor
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Linear Algebra
Mar 1, 2021
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go_editor
1.4k
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gatebt-2021
numerical-answers
linear-algebra
matrices
determinant
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2
GATE2020: 23
The largest eigenvalue of the matrix $\begin{bmatrix} 4 &1 \\ -2& 1 \end{bmatrix}$ is ______________.
soujanyareddy13
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Linear Algebra
Nov 3, 2020
by
soujanyareddy13
2.7k
points
gate2020
numerical-answers
linear-algebra
matrices
eigen-values
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3
GATE2020: 46
The system of linear equations $cx+y=5$ $3x+3y=6$ has no solution when $c$ is equal to _______________________.
soujanyareddy13
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Linear Algebra
Nov 3, 2020
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soujanyareddy13
2.7k
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gate2020
numerical-answers
linear-algebra
system-of-equations
0
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0
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4
GATE2019: 20
Matrix $A=\begin{bmatrix} 0&6 \\ p&0 \end{bmatrix}$ will be skew-symmetric when $p$= ____.
soujanyareddy13
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Linear Algebra
Nov 3, 2020
by
soujanyareddy13
2.7k
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gate2019
numerical-answers
linear-algebra
matrices
0
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0
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5
GATE2016-23
The positive Eigen value of the following matrix is __________. $\begin{bmatrix} 2 & 1 \\ 5 & -2 \end{bmatrix}$
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Linear Algebra
Mar 26, 2018
by
Milicevic3306
7.9k
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gate2016
numerical-answers
linear-algebra
matrices
eigen-values
0
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0
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6
GATE2016-54
The value of determinant $A$ given below is ________. $A = \begin{pmatrix} 5 & 16 & 81 \\ 0 & 2 & 2 \\ 0 & 0 & 16 \end{pmatrix}$
Milicevic3306
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Linear Algebra
Mar 26, 2018
by
Milicevic3306
7.9k
points
gate2016
numerical-answers
linear-algebra
matrices
determinant
0
votes
0
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7
GATE2017-37
The value of $c$ for which the following system of linear equations has an infinite number of solutions is ________ $\begin{bmatrix}1 & 2 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} c \\ 4 \end{bmatrix}$
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Linear Algebra
Mar 26, 2018
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Milicevic3306
7.9k
points
gate2017
numerical-answers
linear-algebra
matrices
system-of-equations
0
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0
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8
GATE2015-34
$\begin{array}{cc} 2x_1+ x_2 = 35 \\ 5x_1 + bx_2 = 7.5 \end{array}$ The system of linear equations in two variables shown above will have infinite solutions, if and only if, $b$ is equal to _________
Milicevic3306
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Linear Algebra
Mar 26, 2018
by
Milicevic3306
7.9k
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gate2015
numerical-answers
linear-algebra
system-of-equations
0
votes
0
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9
GATE2015-39
What are the eigenvalues of the following matrix? $\begin{bmatrix} 1 & 1 \\ -2 & 4 \end{bmatrix}$ $2$ and $3$ $-2$ and $3$ $2$ and $-3$ $-2$ and $-3$
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Linear Algebra
Mar 26, 2018
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Milicevic3306
7.9k
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gate2015
linear-algebra
matrices
eigen-values
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0
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10
GATE2015-52
If $A = \begin{bmatrix} 4 & 2 \\ 1 & 3 \end{bmatrix}$, then $A^2+3A$ will be $\begin{bmatrix} 30 & 20 \\ 10 & 20 \end{bmatrix} \\$ $\begin{bmatrix} 28 & 10 \\ 4 & 18 \end{bmatrix} \\$ $\begin{bmatrix} 31 & 13 \\ 7 & 21 \end{bmatrix} \\$ $\begin{bmatrix} 20 & 10 \\ 5 & 15 \end{bmatrix}$
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Linear Algebra
Mar 26, 2018
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Milicevic3306
7.9k
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gate2015
linear-algebra
matrices
matrix-algebra
0
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11
GATE2014-1
The eigenvalues of A =$\begin{bmatrix} 1&-4\\2 & -3 \end{bmatrix} $are $2\underline{+}i$ $-1, -2$ $-1\underline{+}2i$ non-existent
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Linear Algebra
Mar 26, 2018
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Milicevic3306
7.9k
points
gate2014
linear-algebra
matrices
eigen-values
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0
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12
GATE2014-3
The solution for the following set of equations is, $5x+4y+102=13$ $x+3y+z=7$ $4x2y+z=0$ $x=2,y=1,z=1$ $x=1,y=2,z=0$ $x=1,y=0,z=2$ $x=0,y=1,z=2$
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Linear Algebra
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Milicevic3306
7.9k
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gate2014
linear-algebra
system-of-equations
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0
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13
GATE2014-5
The solution to the following set of equations is $2x+3y=4$ $4x+6y=0$ $x=0,y=0$ $x=2, y=0$ $4x=-6y$ No solution
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Linear Algebra
Mar 26, 2018
by
Milicevic3306
7.9k
points
gate2014
linear-algebra
system-of-equations
0
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0
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14
GATE2013-40
The solution of the following set of equations is $x+2y+3z=20$ $7x+3y+z=13$ $x+6y+2z=0$ $x=-2, y=2, z=8$ $x=2, y=-3, z=8$ $x=2, y=3, z=-8$ $x=8, y=2, z=-3$
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Linear Algebra
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Milicevic3306
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gate2013
linear-algebra
matrices
system-of-equations
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0
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15
GATE2013-20
One of the eigcn values of $P=\begin{bmatrix}10 & -4 \\ 18 & -12\end{bmatrix}$ is $2$ $4$ $6$ $8$
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Linear Algebra
Mar 26, 2018
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Milicevic3306
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gate2013
linear-algebra
matrices
eigen-values
0
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0
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16
GATE2013-17
If $P=\begin{bmatrix}1&1\\2&2\end{bmatrix}, Q=\begin{bmatrix}2&1\\2&2\end{bmatrix}$ and $R=\begin{bmatrix}3&0\\1&3\end{bmatrix}$, which one of the following statements is $TRUE$? $PQ=PR$ $QR= RP$ $OP=RP$ $PO= OR$
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Linear Algebra
Mar 26, 2018
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Milicevic3306
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gate2013
linear-algebra
matrices
matrix-algebra
0
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17
GATE2012-32
What is the rank of the following matrix? $\begin{bmatrix}5 & 3 & -1\\ 6 & 2 & -4 \\14 & 10 & 0 \end{bmatrix}$ $0$ $1$ $2$ $3$
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Linear Algebra
Mar 25, 2018
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Milicevic3306
7.9k
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gate2012
linear-algebra
matrices
rank-of-matrix
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18
GATE2018-21
The determinant of the matrix $\begin{pmatrix} 4 & -6 \\ -3 & 2 \end{pmatrix}$ is _________
gatecse
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Feb 20, 2018
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gatecse
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gate2018
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