Question

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 $\left(\begin{array}{l l }x-y & z \\ 2x-y & w\end{array}\right)$ = $\left(\begin{array}{l l }-1 & 4 \\ 0 & 5\end{array}\right)$ , find the value of x + y.

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

Give an example of a skew symmetric matrix of order 3.

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

Write the degree of the differential equation : $\left({\frac{d^{2}y}{d x^{2}}}\right)^{2}-2{\frac{d^{2}y}{d x^{2}}}-{\frac{d y}{d x}}+1=0.$

What is the degree of the following differential equation ? $5x\biggl(\frac{d y}{d x}\biggr)^{2}-\frac{d^{2}y}{d x^{2}}-6y\;=\log x.$