1
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$A=\left[\begin{array}{cc}k+1 & 2 \\ 4 & k-1\end{array}\right]$$ is a singular matrix, then possible values of $$\mathrm{k}$$ are

A
$$\pm 1$$
B
$$\pm 2$$
C
$$\pm 3$$
D
$$\pm 4$$
2
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } A=\left(\begin{array}{ll} 1 & 2 \\ 0 & 1 \end{array}\right) \quad P=\left(\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right) \quad Q=P^T A P, \quad \text { then } P Q^{2014} P^T \text { is equal to } $$

A
$$ \left(\begin{array}{cc} 1 & 2^{2014} \\ 0 & 1 \end{array}\right) $$
B
$$ \left(\begin{array}{cc} 1 & 4028 \\ 0 & 1 \end{array}\right) $$
C
$$ \left(P^T\right)^{2013} A^{2014} P^{2013} $$
D
$$ P^T A^{2014} P $$
3
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$A$$ and $$B$$ are invertible matrices of the same order such that $$\left|(A B)^{-1}\right|=8$$ if $$|A|=2$$ then $$|B|$$ is

A
6
B
16
C
4
D
$$\frac{1}{16}$$
4
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$2 A+3 B=\left[\begin{array}{ccc}2 & -1 & 4 \\ 3 & 2 & 5\end{array}\right]$$ and $$A+2 B=\left[\begin{array}{lll}5 & 0 & 3 \\ 1 & 6 & 2\end{array}\right]$$ then $$B=$$

A
$$ \left[\begin{array}{ccc} -8 & -1 & -2 \\ 1 & -10 & 1 \end{array}\right] $$
B
$$ \left[\begin{array}{ccc} 8 & 1 & -2 \\ -1 & 10 & -1 \end{array}\right] $$
C
$$ \left[\begin{array}{ccc} 8 & 1 & 2 \\ -1 & 10 & -1 \end{array}\right] $$
D
$$ \left[\begin{array}{ccc} 8 & -1 & 2 \\ -1 & 10 & -1 \end{array}\right] $$
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