Determinants Te...

If $$A=\begin{vmatrix} 1 & -1 & 1\\ 0 & 2 & -3\\ 2 & 1 & 0\end{vmatrix}$$ and $$B=(adj A)$$, and $$C=5A$$, then $$\displaystyle\frac{|adj B|}{|C|}$$ is?

If the determinant $$\Delta =\begin{vmatrix} 3 & -2 & \sin { 3\theta  }  \\ -7 & 8 & \cos { 2\theta  }  \\ -11 & 14 & 2 \end{vmatrix}=0$$, then the value of $$\sin { \theta  } $$ is

If the matrix $$A=\begin{bmatrix} x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z \end{bmatrix},xyz=60$$ and $$8x+4y+3z=10$$, then $$A(adj\quad A)$$ is equal to

If $$A=\begin{bmatrix} x & x-1 \\ 2x & 1 \end{bmatrix}$$ and if $$\text{det}A=-9$$, then the values of $$x$$ are

If $$A=\begin{bmatrix} x & 1 & -x \\ 0 & 1 & -1 \\ x & 0 & 7 \end{bmatrix}$$ and $$det(A)=\begin{vmatrix} 3 & 0 & 1 \\ 2 & -1 & 0 \\ 0 & 6 & 7 \end{vmatrix}$$ then the value of $$x$$ is

If $$A=\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{vmatrix}$$, then the value of $$\left| A \right| \left| adj\left( A \right)  \right| $$ is

If $$A=\begin{bmatrix} 1 & 2 & -1 \\ -1& 1 & 2 \\ 2 & -1 & 1\end{bmatrix}$$, then $$\text{det} (\text{adj}(\text{adj} A))$$ is equal to.

If $$3x+2y=I$$ and $$2x-y=O$$, where $$I$$ and $$O$$ are unit and null matrices of order $$3$$ respectively, then

If $$A = \begin{bmatrix}\cos x & \sin x\\ -\sin x & \cos x\end{bmatrix}$$ and $$A\ adj\ A = k\begin{bmatrix}1 & 0\\ 0 & 1\end{bmatrix}$$ then the value of $$k$$ is

The value of $$a$$, for which the points $$(9, 5), (1, 2)$$ and $$(a, 8)$$ are collinear, is