Question

If $\left(\begin{array}{l l }1 & 0 \\ y & 5\end{array}\right)$ + 2 $\left(\begin{array}{l l }x & 0 \\ 1 & -2\end{array}\right)$ = , where I is a 2×2 unit matrix, find (x – y).

If x ∈ N and $\begin{vmatrix}x+3 & -2 \\ -3x & 2x\end{vmatrix}$ = 8, 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 ${\vec{b}}={\hat{j}}+{\hat{k}}\,.$

Write the differential equation obtained by eliminating the arbitrary constant C in the equation representing the family of curves xy = C cos x.

If A = $\left(\begin{array}{l l l }1 & 2 & 2 \\ 2 & 1 & x \\ -2 & 2 & -1\end{array}\right)$ is a matrix satisfying AA’ = 9I, find x.

If A = $\left(\begin{array}{l l }3 & 10 \\ 2 & 7\end{array}\right)$ , then write A⁻¹.

If $\begin{vmatrix} \sin\alpha & \cos\beta \\ \cos\alpha & \sin\beta \end{vmatrix} =-\ {\begin{array}{l}{1}\\ {2}\end{array}}\$ , write the value of x.