Question

If A is a matrix of order 3 x 4 and B is a matrix of order 4 x 3, then find order of matrix (AB.)

If $\left(\begin{array}{l l }2x+y & 3y \\ 0 & 4\end{array}\right)$ = $\left(\begin{array}{l l }6 & 0 \\ 0 & 4\end{array}\right)$ then find the value of x.

Write the number of vectors of unit length perpendicular to both the vector $\stackrel{\rightarrow}{a}=\stackrel{\wedge}{2i}+\stackrel{\wedge}{j}+\stackrel{\wedge}{2k}$ and ${\vec{b}}={\hat{j}}+{\hat{k}}\,.$

If for any 2 × 2 square matrix A, A(adj A) = $\left(\begin{array}{l l }8 & 0 \\ 0 & 8\end{array}\right)$ , then write the value of |A|.

If $\left(\begin{array}{l l }1 & 2 \\ 3 & 4\end{array}\right)$ $\left(\begin{array}{l l }3 & 1 \\ 2 & 5\end{array}\right)$ = $\left(\begin{array}{l l }7 & 11 \\ k & 23\end{array}\right)$ , then write the value of k.

Write the value of the determinant $\begin{vmatrix}p & p+1 \\ p-1 & p\end{vmatrix}$

Write the degree of the differential equation : $\left(\frac{d y}{d x}\right)^{4}+3x\frac{d^{2}y}{d x^{2}}=0.$