Question

Find the sum of the vectors $\stackrel{\rightarrow}{a}=\hat{i}-2\hat{j}+\hat{k}\;,$ $\vec{b}=-2\hat{i}+4\hat{j}+5\hat{k}$ and $\stackrel{\rightarrow}{c}=\hat{i}-6\hat{j}-7\hat{k}.$

Let A and B are matrices of order 3 x 2 and 2 x 4 respectively. Write the order of matrix (AB).

P and Q are two points with position vectors $3\stackrel{\rightarrow}{a}-2\stackrel{\rightarrow}{b}$ and $\stackrel{\rightarrow}{a}+\stackrel{\rightarrow}{b}$ respectively. Write the position vector of a point R which divides the line segment PQ externally in the ratio 2 : 1.

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

Write the order of product matrix $\left(\begin{array}{l }1 \\ 2 \\ 3\end{array}\right)$ $\left(\begin{array}{l l l }2 & 3 & 4\end{array}\right)$

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

If A = $\left(\begin{array}{l l }cosα & -sinα \\ sinα & cosα\end{array}\right)$ , then for what value of a, A is an identity matrix ?