1
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
$$\frac{1}{19}$$
2
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
$$\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & 2 \\ 3 & 2 & 4\end{array}\right]$$
3
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
4
MHT CET 2021 22th September Evening Shift
+2
-0

If $$A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]$$ and $$A$$ adj $$A=A A^T$$, then $$5 a+b=$$

A
13
B
4
C
$$-$$1
D
5
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