1
MHT CET 2021 23rd September Evening Shift
+2
-0

Which of the following matrices are invertible?

\begin{aligned} & \mathrm{A}=\left[\begin{array}{cc} 2 & 3 \\ 10 & 15 \end{array}\right], \mathrm{B}=\left[\begin{array}{ccc} 1 & 2 & 3 \\ 2 & -1 & 3 \\ 1 & 2 & 3 \end{array}\right], \mathrm{C}=\left[\begin{array}{lll} 1 & 2 & 3 \\ 3 & 4 & 5 \\ 4 & 6 & 8 \end{array}\right], \mathrm{D}=\left[\begin{array}{lll} 2 & 4 & 2 \\ 1 & 1 & 0 \\ 1 & 4 & 5 \end{array}\right] \end{aligned}

A
both A and B
B
only C
C
only A
D
only D
2
MHT CET 2021 23th September Morning Shift
+2
-0

If $$A=\left[\begin{array}{rr}2 & 3 \\ 5 & -2\end{array}\right]$$ and $$A^{-1}=K A$$, then $$K$$ is

A
19
B
$$\frac{-1}{19}$$
C
$$-19$$
D
$$\frac{1}{19}$$
3
MHT CET 2021 23th September Morning Shift
+2
-0

If $$\mathrm{A}=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$$, then $$\mathrm{A}(\operatorname{adj} \mathrm{A})=$$

A
$$\left[\begin{array}{ccc}-1 / 3 & 0 & 0 \\ 0 & -1 / 3 & 0 \\ 0 & & -1 / 3\end{array}\right]$$
B
$$\left[\begin{array}{lll}3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3\end{array}\right]$$
C
$$\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$$
D
$$\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & 2 \\ 3 & 2 & 4\end{array}\right]$$
4
MHT CET 2021 23th September Morning Shift
+2
-0

If $$A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & -1 & 0 \\ 3 & 3 & -4\end{array}\right], B=\left[\begin{array}{l}1 \\ 1 \\ 2\end{array}\right]$$ and $$X=\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right]$$ such that $$A X=B$$, then the value of $$x_1+x_2+x_3=$$

A
4
B
5
C
6
D
3
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