Determinants Te...

If $$P = \begin{bmatrix} 1& 2 & 1\\ 1 & 3 & 1\end{bmatrix}, Q = PP^{T}$$, then the value of the determinant of $$Q$$ is

Evaluate $$\begin{vmatrix} \cos 15^o& \sin 15^o\\ \sin 75^o & \cos 75^o\end{vmatrix}$$

Let $$A$$ be a $$3 \times 3$$ matrix and $$B$$ be its adjoint matrix. If $$|B| = 64$$, then $$|A| =$$

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

If a, b and c are in A, P., then the value of $$\begin{vmatrix}
x+2 & x+3 &x+a \\
 x+4& x+5 &x+b \\
x+6 & x+7 & x+c
\end{vmatrix}$$ is.

If $$\Delta_r = \begin{vmatrix}2r - 1 & ^mC_r & 1\\ m^2 - 1 & 2^m & m+1\\ sin^2(m^2) & sin^2(m) & sin^2(m+1)\end{vmatrix}$$, then the value of $$\displaystyle \sum_{r = 0}^m \Delta_r$$, is

The value of the determinant $$\begin{vmatrix}1 & \cos (\alpha - \beta) & \cos \alpha\\ \cos(\alpha - \beta) & 1 & \cos \beta\\ \cos \alpha & \cos \beta & 1\end{vmatrix}$$ is

The value of the determinant $$\begin{vmatrix}cos\, \alpha  & -sin \,\alpha   &1 \\ sin \, \alpha  & cos \, \alpha  & 1\\ cos (\alpha +\beta)  & -sin (\alpha +\beta ) & 1\end{vmatrix} $$ is

The centre of a circle is $$(-6,4)$$. If one end of the diameter of the circle is at $$(-12,8)$$, then the other end is at

If $$A(x)=\begin{vmatrix} x+1 & 2x+1 & 3x+1 \\ 2x+1 & 3x+1 & x+1 \\ 3x+1 & x+1 & 2x+1 \end{vmatrix}$$ 
then $$\displaystyle \int _{ 0 }^{ 1 }{ A(x) } dx=$$