Determinants Te...

The point $$(-a,-b),(0,0),(a,b)$$ and $$(a^{2},ab)$$ are-

$$A=\begin{bmatrix} 5 & 5a & a \\ 0 & a & 5a \\ 0 & 0 & 5 \end{bmatrix}$$ If $$\left| A^{ 2 } \right| =25$$ then $$|a|=$$

The value of (adj $$A$$) is equal to

Two points $$(a, 0)$$ and $$(0, b)$$ are joined by a straight line. Another point on this line is

First row of the matrix $$A$$ is $$\begin{bmatrix}1& 3 & 2\end{bmatrix}$$. If $$adj (A)$$ =\begin{bmatrix}-2 & 4 & a\\ -1& 2 & 1\\ 3a& -5 &-2 \end{bmatrix} then a possible value of $$det(A)$$ is

$$\begin{vmatrix} 2^3 & 3^3 & 3.2^2+3.2+1\\ 3^3 & 4^3 & 3.3^2+3.3+1\\ 4^3 & 5^3 & 3.4^2+3.4+1\end{vmatrix}$$ is equal to?

If $$P=\begin{bmatrix} 1 & \alpha & 3\\ 1 & 3 & 3\\ 2 & 4 & 4\end{bmatrix}$$ is a $$3\times 3$$ matrix A and $$|A|=4$$, then $$\alpha$$ is equal to?

The determinant $$\left| {\begin{array}{*{20}{c}}a&b&{a\alpha  + b}\\b&c&{b\alpha  + c}\\{a\alpha  + b}&{b\alpha  + c}&0\end{array}} \right|$$ is equal to zero, if-

$$A = \left[ \begin{array}{l}1\,\,\,\,\,\,\,\,1\\3\,\,\,\,\,\,\,4\end{array} \right]$$ and $$A\left( {adj\,A} \right) = KI$$, then the value of $$'K'$$

The value of determinant $$ \begin{vmatrix} 19 & 6 & 7 \\ 21 & 3 & 15 \\ 28 & 11 & 6 \end{vmatrix} $$ is :