Question

If A = $\left(\begin{array}{l l }2 & 3 \\ 1 & -4\end{array}\right)$ , B = $\left(\begin{array}{l l }1 & -2 \\ -1 & 3\end{array}\right)$ , verify that $(A B)^{-1}=B^{-1}A^{-1}$

If A = $\left(\begin{array}{l l }1 & -1 \\ 2 & -1\end{array}\right)$ , B = $\left(\begin{array}{l l }a & 1 \\ b & -1\end{array}\right)$ and (A + B)² = A²+ B², then find the values of a and b.

For the following matrices A and B, verify that [AB]’ = B’A’ where, A = $\left(\begin{array}{l }1 \\ -4 \\ 3\end{array}\right)$ , B = $\left(\begin{array}{l l l }-1 & 2 & 1\end{array}\right)$

Using properties of determinants, prove that : $\begin{vmatrix}1 & 1+p & 1+p+q \\ 3 & 4+3p & 2+4p+3p \\ 4 & 7+4p & 2+7p+4q\end{vmatrix}$ = 1

The equation of tangent at (2, 3) on the curve y² = ax³ + b is y = 4x – 5. Find the values of a and b.

Solve the differential equation given as : $\left(\frac{e^{-2\sqrt{x}}}{\sqrt{x}}-\frac{y}{\sqrt{x}}\right)\frac{d x}{d y}\;=1,x\neq0$

Find the approximate value of f(3·02), up to 2 places of decimal, where f(x) = 3x² + 5x + 3.