Question

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

If the following function f(x) is continuous at x = 0, then write the value of k.

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).

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.

If A' = $\left(\begin{array}{l l }3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right)$ and B = $\left(\begin{array}{l l l }-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right)$ then find A' – B'.

If A and B are invertible matrices of order 3, $|\mathbf{A}|=$ 2 and $|(\mathbf{AB})^{-1}|\,=\,-{\frac{1}{6}}.$ Find $|\mathbf{B}$.

Let A = $A\ =\ {\left(\begin{array}{l l}{2}&{-1}\\ {3}&{4}\end{array}\right)}$ , B = $A\ =\ {\left(\begin{array}{l l}{5}&{2}\\ {7}&{4}\end{array}\right)}$ , C = $A\ =\ {\left(\begin{array}{l l}{2}&{5}\\ {3}&{8}\end{array}\right)}$ , find a matrix D such that CD - AB = 0.