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.

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,

If m and n are the order and degree, respectively of the differential equation $\textstyle y\left({\frac{d y}{d x}}\right)^{3}+x^{3}\left({\frac{d^{2}y}{d x^{2}}}\right)^{2}-x y$= sin x, then write the value of m + n.

If ${\left[\begin{array}{l l}{x y}&{4}\\ {z+6}&{x+y}\end{array}\right]}\ ={\left[\begin{array}{l l}{8}&{w}\\ {0}&{6}\end{array}\right]},$ write the value of x + y + z.

If $\left(\begin{array}{l l }x-y & 2y \\ 2y+z & x+y\end{array}\right)$ = $\left(\begin{array}{l l }1 & 4 \\ 9 & 5\end{array}\right)$

Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.

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