Question

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

If A = $\left(\begin{array}{l l l }1 & 2 & 2 \\ 2 & 1 & x \\ -2 & 2 & -1\end{array}\right)$ is a matrix satisfying AA’ = 9I, find x.

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

Solve the following matrix equation for x : [x 1] $\left(\begin{array}{l l }1 & 0 \\ -2 & 0\end{array}\right)$ = 0.

Write the integrating factor of the differential equations ${\sqrt{x}}{\frac{d y}{d x}}+y=e^{-2{\sqrt{x}}}\,.$

If $\left(\begin{array}{l l }x-y & z \\ 2x-y & w\end{array}\right)$ = $\left(\begin{array}{l l }-1 & 4 \\ 0 & 5\end{array}\right)$ , find the value of x + y.

If $\stackrel{\rightarrow}{a}\$ =$4\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}\$ =$2\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ then find a unit vector parallel to the vector $\stackrel{\rightarrow}{a}+\stackrel{\rightarrow}{b}$