Question

Let R be the equivalence relation in the set A = {0, 1, 2, 3, 4, 5} given by R = {(a, b) : 2 divides (a –b)}. Write the equivalence class [0].

If A = $\left(\begin{array}{l l }cosα & -sinα \\ sinα & cosα\end{array}\right)$ , then for what value of a, A is an identity matrix ?

If matrix A = $\left(\begin{array}{l l }2 & -2 \\ -2 & 2\end{array}\right)$ and A² = pA, then write the value of p.

If $\begin{vmatrix}x+1 & x-1 \\ x-3 & x+2\end{vmatrix}$ = $\begin{vmatrix}4 & -1 \\ 1 & 3\end{vmatrix}$ , then write the value of x.

If A = $\left(\begin{array}{l l }4 & 6 \\ 7 & 5\end{array}\right)$ , then what is the value of $\ A{\cdot}(a d j A)$ ?

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

If $\stackrel{\wedge}{\mathrm{a}}$, $\stackrel{\wedge}{\mathrm{b}}$ and $\stackrel{\wedge}{\mathrm{c}}$ are mutually perpendicular unit vectors, then find value of $|2\stackrel{\wedge}{\mathrm{a}}$ + $\stackrel{\wedge}{\mathrm{b}}$ + $\stackrel{\wedge}{\mathrm{c}}|$.