1
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$A=\left[\begin{array}{ccc}0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x\end{array}\right]$$ is a singular matrix then $$x$$ is equal to

A
$$-12$$
B
21
C
$$-144$$
D
144
2
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } P=\left[\begin{array}{lll} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{array}\right] \text { is the adjoint of a } 3 \times 3 \text { matrix } A \text { and }|A|=4 \text { then } \alpha \text { is equal to } $$

A
11
B
4
C
0
D
5
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$A=\left[\begin{array}{ccc}-1 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right]$$ then the inverse of $$(A I)^t$$ (where $$\mathrm{I}$$ is an identity matrix) is

A
$$ \left[\begin{array}{ccc} 1 & -8 & 5 \\ -1 & 7 & -4 \\ 1 & -5 & 3 \end{array}\right] $$
B
$$ \left[\begin{array}{ccc} -1 & 1 & -1 \\ 8 & -7 & 5 \\ -5 & 4 & -3 \end{array}\right] $$
C
$$ \left[\begin{array}{ccc} 1 & 8 & -5 \\ -1 & 7 & -4 \\ 0 & 5 & 3 \end{array}\right] $$
D
$$ \left[\begin{array}{ccc} 1 & -1 & 1 \\ -8 & 7 & -5 \\ 5 & -4 & 3 \end{array}\right] $$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } x, y, z \text { are non zero real numbers, then inverse of matrix } A=\left[\begin{array}{lll} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{array}\right] \text { is } $$

A
$$ \frac{1}{x y z}\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right] $$
B
$$ \left[\begin{array}{ccc} 1 / x & 0 & 0 \\ 0 & 1 / y & 0 \\ 0 & 0 & 1 / z \end{array}\right] $$
C
$$ x y z\left[\begin{array}{ccc} 1 / x & 0 & 0 \\ 0 & 1 / y & 0 \\ 0 & 0 & 1 / z \end{array}\right] $$
D
$$ \frac{1}{x y z}\left[\begin{array}{lll} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{array}\right] $$
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