Question

If $\left(\begin{array}{l l l }2 & 1 & 3\end{array}\right)$ $\left(\begin{array}{l l l }-1 & 0 & -1 \\ -1 & 1 & 0 \\ 0 & 1 & 1\end{array}\right)$ $\left(\begin{array}{l }1 \\ 0 \\ -1\end{array}\right)$ = A , then write the order of matrix A.

If $\left(\begin{array}{l l }2 & 3 \\ 5 & 7\end{array}\right)$ $\left(\begin{array}{l l }1 & -3 \\ -2 & 4\end{array}\right)$ = $\left(\begin{array}{l l }-4 & 6 \\ -9 & x\end{array}\right)$ , write the value of x.

Write a unit vector in the direction of vector $\stackrel{\rightarrow}{PQ}\$ where $\stackrel{\rightarrow}{p}\$ and $\stackrel{\rightarrow}{q}\$ are the points (1, 3, 0) and (4, 5, 6),respectively,

Write the solution of the differential equation ${\frac{d y}{d x}}=2^{-y}.$

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'.

Write the value of $\textstyle\int\!{\frac{\ d x}{x^{2}+16}}$

Find matrix A such that. $\left(\begin{array}{l l}{2}&{-1}\\ {1}&{0}\\ {-3}&{4}\end{array}\right)$ $A={\left(\begin{array}{l l}{-1}&{-8}\\ {1}&{-2}\\ {9}&{22}\end{array}\right)}$