Question

Evaluate $\textstyle\int$ sin³ x dx.

If $\left(\begin{array}{l l }2 & 3 \\ 5 & 7\end{array}\right)$ $\left(\begin{array}{l l }1 & -3 \\ -2 & 4\end{array}\right)$ = $\left(\begin{array}{l l }-4 & 6 \\ -9 & x\end{array}\right)$ , write the value of x.

Let A and B are matrices of order 3 x 2 and 2 x 4 respectively. Write the order of matrix (AB).

Find the matrix A if $\left(\begin{array}{l l l }9 & -1 & 4 \\ -2 & 1 & 3\end{array}\right)$ = A + $\left(\begin{array}{l l l }1 & 2 & -1 \\ 0 & 4 & 9\end{array}\right)$

If f : R → R defined as f(x) =${\frac{2x-7}{4}}\ $ is an invertible function, write $f^{-1}(x).$

Find the sum of the vectors $\stackrel{\rightarrow}{a}=\hat{i}-2\hat{j}+\hat{k}\;,$ $\vec{b}=-2\hat{i}+4\hat{j}+5\hat{k}$ and $\stackrel{\rightarrow}{c}=\hat{i}-6\hat{j}-7\hat{k}.$

Find matrix A such that. $\left(\begin{array}{l l}{2}&{-1}\\ {1}&{0}\\ {-3}&{4}\end{array}\right)$ $A={\left(\begin{array}{l l}{-1}&{-8}\\ {1}&{-2}\\ {9}&{22}\end{array}\right)}$