Determinants Te...

If $$\Delta_1=\begin{vmatrix} x & b & b\\ a & x & b\\ a & a & x\end{vmatrix}$$ and $$\Delta_2=\begin{vmatrix} x & b\\ a & x\end{vmatrix}$$ are the given determinants, then.

If a, b, c are different and $$\begin{vmatrix} 0 & x-a & x-b \\ x+a & 0 & x-c\\ x+b & x+c & 0\end{vmatrix}=0$$, then x is equal to.

If $$\left |\begin{array}{111}6i & -3i & 1 \\4 & 3i & -1 \\20 & 3 & i \\\end {array}\right | =x+iy$$, then

If A = $$\begin{bmatrix}
              a & 0 & 0 \\[0.3em]
              0 & a & 0 \\[0.3em]
              0 & 0 & a
              \end{bmatrix}$$, then the value of |A| |Adj. A|

If $$f(x) =$$ $$
\left |
\begin{array}{111}
1 & x & x+1 \\
2x & x(x-1) & (x+1)x \\
3x(x-1) & x(x-1)(x-2) & (x+1)x(x-1) \\
\end {array}
\right |
$$
then f(100) is equal to

If A = $$\begin{bmatrix}
              a & 0 & 0 \\[0.3em]
              0 & a & 0 \\[0.3em]
              0 & 0 & a
              \end{bmatrix}$$, then the value of  |Adj. A| is equal to

If A = $$ \begin{bmatrix} \alpha & 2 \\ 2 & \alpha\end{bmatrix}$$ and | A$$^3$$ | = 125 then $$\alpha$$ is 

If the points $$(-2, -5), (2, -2), (8, a)$$ are collinear, then the value of $$a$$ is ________.

If $$ \begin{vmatrix}a & a & x \\ m & m & m \\b & x & b\end{vmatrix}=0$$  then $$x$$ is:

The points $$(-a, -b), (0, 0), (a, b)$$ $$(a^2,ab)$$  are