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Questions without answers in Linear Algebra

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1
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 __________.
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 __________.
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GATE2020: 23
The largest eigenvalue of the matrix $\begin{bmatrix} 4 &1 \\ -2& 1 \end{bmatrix}$ is ______________.
The largest eigenvalue of the matrix $\begin{bmatrix} 4 &1 \\ -2& 1 \end{bmatrix}$ is ______________.
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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 _______________________.
The system of linear equations$$cx+y=5$$$$3x+3y=6$$has no solution when $c$ is equal to _______________________.
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4
GATE2019: 20
Matrix $A=\begin{bmatrix} 0&6 \\ p&0 \end{bmatrix}$ will be skew-symmetric when $p$= ____.
Matrix $A=\begin{bmatrix} 0&6 \\ p&0 \end{bmatrix}$ will be skew-symmetric when $p$= ____.
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5
GATE2016-23
The positive Eigen value of the following matrix is __________. $\begin{bmatrix} 2 & 1 \\ 5 & -2 \end{bmatrix}$
The positive Eigen value of the following matrix is __________. $$\begin{bmatrix} 2 & 1 \\ 5 & -2 \end{bmatrix}$$
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6
GATE2016-54
The value of determinant $A$ given below is ________. $A = \begin{pmatrix} 5 & 16 & 81 \\ 0 & 2 & 2 \\ 0 & 0 & 16 \end{pmatrix}$
The value of determinant $A$ given below is ________.$A = \begin{pmatrix} 5 & 16 & 81 \\ 0 & 2 & 2 \\ 0 & 0 & 16 \end{pmatrix}$
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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 ________ $\begin{bmatrix}1 & 2 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} c \\ 4 \end{bmatrix}$
The value of $c$ for which the following system of linear equations has an infinite number of solutions is ________ $$\begin{bmatrix}1 & 2 \\ 1 & 2 \end{bmatrix} \begin{b...
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8
GATE2015-34
$\begin{array}{cc} 2x_1+ x_2 = 35 \\ 5x_1 + bx_2 = 7.5 \end{array}$ The system of linear equations in two variables shown above will have infinite solutions, if and only if, $b$ is equal to _________
$$\begin{array}{cc} 2x_1+ x_2 = 35 \\ 5x_1 + bx_2 = 7.5 \end{array}$$ The system of linear equations in two variables shown above will have infinite solutions, if and onl...
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9
GATE2015-39
What are the eigenvalues of the following matrix? $\begin{bmatrix} 1 & 1 \\ -2 & 4 \end{bmatrix}$ $2$ and $3$ $-2$ and $3$ $2$ and $-3$ $-2$ and $-3$
What are the eigenvalues of the following matrix? $$\begin{bmatrix} 1 & 1 \\ -2 & 4 \end{bmatrix}$$$2$ and $3$$-2$ and $3$$2$ and $-3$$-2$ and $-3$
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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
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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12
GATE2014-3
The solution for the following set of equations is, $5x+4y+102=13$ $x+3y+z=7$ $4x2y+z=0$ $x=2,y=1,z=1$ $x=1,y=2,z=0$ $x=1,y=0,z=2$ $x=0,y=1,z=2$
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$$x=0,y=1,z=2$
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13
GATE2014-5
The solution to the following set of equations is $2x+3y=4$ $4x+6y=0$ $x=0,y=0$ $x=2, y=0$ $4x=-6y$ No solution
The solution to the following set of equations is$$2x+3y=4$$$$4x+6y=0$$$x=0,y=0$$x=2, y=0$$4x=-6y$No solution
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14
GATE2013-40
The solution of the following set of equations is $x+2y+3z=20$ $7x+3y+z=13$ $x+6y+2z=0$ $x=-2, y=2, z=8$ $x=2, y=-3, z=8$ $x=2, y=3, z=-8$ $x=8, y=2, z=-3$
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$$x=8, y=2, z=-3$
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15
GATE2013-20
One of the eigcn values of $P=\begin{bmatrix}10 & -4 \\ 18 & -12\end{bmatrix}$ is $2$ $4$ $6$ $8$
One of the eigcn values of $P=\begin{bmatrix}10 & -4 \\ 18 & -12\end{bmatrix}$ is$2$$4$$6$$8$
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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 $TRUE$? $PQ=PR$ $QR= RP$ $OP=RP$ $PO= OR$
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...
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17
GATE2012-32
What is the rank of the following matrix? $\begin{bmatrix}5 & 3 & -1\\ 6 & 2 & -4 \\14 & 10 & 0 \end{bmatrix}$ $0$ $1$ $2$ $3$
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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18
GATE2018-21
The determinant of the matrix $\begin{pmatrix} 4 & -6 \\ -3 & 2 \end{pmatrix}$ is _________
The determinant of the matrix $\begin{pmatrix} 4 & -6 \\ -3 & 2 \end{pmatrix}$ is _________
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