Determinants Te...

If $$a, b, c \ \epsilon \ R$$, find the number of real roots of the equation given by $$ \Delta = 0 $$, where  
$$\Delta =\begin{vmatrix}
x & c & -b\\
-c & x & a\\
b & -a & x
\end{vmatrix}$$.

If $$A=\begin{bmatrix} 0&\sin \alpha   & \sin \alpha\sin \beta \\-\sin \alpha &0  &\cos \alpha \sin \beta  \\-\sin \alpha \sin \beta  &-\cos \alpha \cos \beta   &0 \end{bmatrix}$$, then which of the following is true?

For which value of '$$k$$' the points $$(7, -2), (5, 1), (3, k)$$ are collinear?

If $$(3,2)$$, $$(4,k)$$ and $$(5,3)$$ are collinear, then $$k$$ is equal to:

Let $$A$$ be a non-singular matrix. Then $$\left| adjA \right| $$ is equal to

The value of the determinant $$\begin{vmatrix} -a& b & c\\ a & -b &c \\ a & b &-c \end{vmatrix}$$ is equal to

If $$D_p=\begin{vmatrix} p& 15 & 8\\ p^2 & 35 & 9\\ p^3 & 25 & 10\end{vmatrix}$$, then $$D_1+D_2+D_3+D_4+D_5$$ is equal to

$$\displaystyle a_{0}$$ equals

If $$A=\begin{bmatrix} 4 & 2 \\ 3 & 3 \end{bmatrix}$$, then adj (adj $$A$$) is equal to

A set of points which lie on same line are called as