Question

Find the value of a if $\left(\begin{array}{l l }a-b & 2a+c \\ 2a-b & 3c+d\end{array}\right)$ = $\left(\begin{array}{l l }-1 & 5 \\ 0 & 13\end{array}\right)$ .

Find the sum of the vectors : $\stackrel{\rightarrow}{a}=\hat{i}-3\hat{k},$ ${\vec{b}}=2{\hat{j}}-{\hat{k}},$ $\stackrel{\rightarrow}{c}=2\hat{i}-3\hat{j}+2\hat{k}.$

If f : R → R is defined by f(x) = 3x + 2, then define f [f(x)].

Find a vector in the direction of vector $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +6\stackrel{\wedge}{k}$which has magnitude 21 units.

Given A = $\left(\begin{array}{l l l }4 & 2 & 5 \\ 2 & 0 & 3 \\ -1 & 1 & 0\end{array}\right)$ , write the value of det. $(2A A^{-1}).$

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).

Write the element $a_{23}$ of a 3 × 3 matrix A = ($a_{i j}$) whose elements $a_{i j}$ are given by $a_{i j}=\frac{|i-j|}{2}$