Question

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

For a 2 x 2 matrix, A = [$a_{i j}$] whose elements are given by $a_{i j}$ = $i/j,$ write the value of $a_{12}\,.$

Write the differential equation formed from the equation y = mx + c, where m and c are arbitrary constants.

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

Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.

If $\left(\begin{array}{l l }1 & 2 \\ 3 & 4\end{array}\right)$ $\left(\begin{array}{l l }3 & 1 \\ 2 & 5\end{array}\right)$ = $\left(\begin{array}{l l }7 & 11 \\ k & 23\end{array}\right)$ , then write the value of k.

Write the value of : $\textstyle\int{\frac{x+\cos6.x}{3\,x^{2}\,+\,\sin6.x}}\,d x\,.$