Question

Find the maximum value of $\begin{vmatrix}1 & 1 & 1 \\ 1 & 1+sinθ & 1 \\ 1 & 1 & 1+cosθ\end{vmatrix}$

If A = $\left(\begin{array}{l l l }1 & 2 & 2 \\ 2 & 1 & x \\ -2 & 2 & -1\end{array}\right)$ is a matrix satisfying AA’ = 9I, find x.

If $\left(\begin{array}{l l }2x+1 & 2y \\ 0 & y²+1\end{array}\right)$ = $\left(\begin{array}{l l }x+3 & 10 \\ 0 & 26\end{array}\right)$ , write the value of (x + y).

Write the order of product matrix $\left(\begin{array}{l }1 \\ 2 \\ 3\end{array}\right)$ $\left(\begin{array}{l l l }2 & 3 & 4\end{array}\right)$

Find a unit vector in the direction of $\stackrel{\rightarrow}{A}$ = $3\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +6\stackrel{\wedge}{k}$

If $\left(\begin{array}{l l }2x & 3\end{array}\right)$ $\left(\begin{array}{l l }1 & 2 \\ -3 & 0\end{array}\right)$ $\left(\begin{array}{l }x \\ 3\end{array}\right)$ = 0,

Solve the following matrix equation for x : [x 1] $\left(\begin{array}{l l }1 & 0 \\ -2 & 0\end{array}\right)$ = 0.