State whether the system 3x+y+z=8; -x+y-2z=-5; x+y+z=6; -2x+2y-3z=-7 is consistant or not and the nature of the solution

For the function f(z)= \frac{tan z}{z} , z=0 is a 

The residue of f(z)= \frac{1}{(z^2+1)^2} about the pole z=i is

By Cayley -Hamilton theorem the matrix A= \left( \begin{matrix} 1 & 3&7 \\ 4 & 2 &3\\1 & 2&1 \end{matrix} \right) satisfies  the characteristic equation----------

The vectors u_1=(1,-2, 3, 4), u_2= (-2, 4 , -1, -3)  and u_3=(-1, 2 ,7 ,6) are

The value of the integral \int_{C}^{}{ \frac{z}{z-2} dz} , C: |z|=1   is 

Solve the simultaneous system of equations by Gauss Jordon Method

5x_1+x_2+x_3+x_4=4 ; x_1+7x_2+x_3+x_4=12 ; x_1+x_2+6x_3+x_4=-5 ~and ~x_1+x_2+x_3+4x_4=-6 ;

then the solution is

Evaluvating \int_{-\infty}^{\infty}{ \frac{x^2}{(x^2+1)^2(x^2+2x+2)} dx} by contour integration, state the poles in side C -contour real axis from -R to +R and Semicircle S above the real axis 

The sum of the Eigen values of  inverse of the matrix A= \left( \begin{matrix} 3 & 0&0 \\ 8 & 4&0\\6 & 2&5 \end{matrix} \right) is