Question

Write the inverse of the matrix $\left(\begin{array}{l l }cosθ & -sinθ \\ sinθ & cosθ\end{array}\right)$ .

The value of the determinant of a matrix A of order 3 × 3 is 4. Find the value of |5A|.

If matrix A = [1 2 3], then write AA’.

If A = $\left(\begin{array}{l l }x & x-y \\ 2x+y & 7\end{array}\right)$ = $\left(\begin{array}{l l }3 & 1 \\ 8 & 7\end{array}\right)$ , then find the value of y.

If $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$ are perpendicular vectors, $|\stackrel{\rightarrow}{a}\$ + $\stackrel{\rightarrow}{b}|\$ = 13 and $|\stackrel{\rightarrow}{a}|\$ =5,find the value of $|\stackrel{\rightarrow}{b}|\$.

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 $\stackrel{\rightarrow}{c}=\hat{i}-6\hat{j}-7\hat{k}.$

If the determinant of matrix A of order 3 × 3 is of value 4, write the value of |3A|.