Question

If A is a square matrix and | A | = 2, then write the value of | AA’ |, where A’ is the transpose of matrix A.

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).

Evaluate $\textstyle\int\!{\frac{x^{3}-x^{2}+x-1}{x-1}}\,d x\,.$

If $\begin{array}{l l}{{\vec{a}=x\,\hat{i}+2\,\hat{j}-z\,\hat{k}~}}&{{\mathrm{and}~~~~\vec{b}=3\,\hat{i}-y\,\hat{j}+\hat{k}}}\end{array}$ are two equal vectors, then write the value of x + y + z.

Write the degree of the differential equation $\left({\frac{d^{2}s}{d t^{2}}}\right)^{2}+\left({\frac{d s}{d t}}\right)^{3}+4=0.$

If $\begin{vmatrix} \sin\alpha & \cos\beta \\ \cos\alpha & \sin\beta \end{vmatrix} =-\ {\begin{array}{l}{1}\\ {2}\end{array}}\$ where α and β are acute angles, then write the value of α + β .

Write the value of $\begin{vmatrix}2 & 7 & 65 \\ 3 & 8 & 75 \\ 5 & 9 & 86\end{vmatrix}$