Question

If 2 $\left(\begin{array}{l l }3 & 4 \\ 5 & x\end{array}\right)$ + $\left(\begin{array}{l l }1 & y \\ 0 & 5\end{array}\right)$ = $\left(\begin{array}{l l }7 & 0 \\ 10 & 5\end{array}\right)$ find x - y.

Write the position vector of the point which divides the join of points with position vectors $3\stackrel{\rightarrow}{a}-2\stackrel{\rightarrow}{b}$ and $2\stackrel{\rightarrow}{a}+3\stackrel{\rightarrow}{b}$ in the ratio 2:1.

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

Write a vector in the direction of the vector $\displaystyle{\hat{\iota}}-2\,{\hat{\iota}}+2\,{\hat{\iota}}$ that has magnitude 9 units.

If 2 $\left(\begin{array}{l l }1 & 3 \\ 0 & x\end{array}\right)$ + $\left(\begin{array}{l l }y & 0 \\ 1 & 2\end{array}\right)$ = $\left(\begin{array}{l l }5 & 6 \\ 1 & 8\end{array}\right)$ , write the value of (x + y).

If A is a 3 × 3 matrix, $|A|\neq0$ and $|3A|\,=\,k|A|,$ then write the value of k.

Evaluate : $\textstyle\int\!{\frac{\ d x}{\sin^{2}x\cos^{2}x}}$ .