If A = \(\begin{bmatrix}3 & -1 & 1 \\ -15 & 6 & -5\\5 & -2 & 2 \end{bmatrix}\) then, find the Inverse of A.

Solve by matrix inversion method: x - y + 2z = 3; 2x + z = 1; 3x + 2y + z = 4.

Find adjoint of \(A=\left[ \begin{matrix} 1 & -2 & -3 \\ 0 & 1 & 0 \\ -4 & 1 & 0 \end{matrix} \right] \)

Resolve into partial fractions for the following : \(\frac{x+2}{(x-1)(x+3)^2}\)

By the principle of mathematical induction, prove the following.
aⁿ - bⁿ is divisible by a - b, for all \(n\in N\) .

The profit Rs.y accumulated in thousand in x months is given by y = -x²  + 10x - 15. Find the best time to end the project.

If \(\sin { A } =\frac { 3 }{ 5 } \) 0 < A < \(\frac{\pi}{2}\)  and \(\cos { B } =\frac { -12 }{ 13 } \) , π < B < \(\frac{3\pi}{2}\) find the values of the following \(\cos (A+B)\)

If cosec A + sec A = cosec B + sec B, prove that cot\(\left( \frac { A+B }{ 2 } \right) \) = tanA tanB

Examine the following functions for continuity at indicated points
\(f(x)=\left\{\begin{array}{cl} \frac{x^2-4}{x-2}, & \text { if } x \neq 2 \\ 0, & \text { if } x=2 \end{array} \right.\) at x = 2

Draw the graph of the function f(x) = x² - 5.