DUE DATE: March $23,201817$:$00$

Let $A=\left[\begin{array}{ccc}10& 2& -1\\ -3& -6& 2\\ 1& 1& 5\end{array}\right]$ and $b=\left[\begin{array}{c}27\\ -61\mathrm{.}5\\ -21\mathrm{.}5\end{array}\right].$

a$.$ Solve the system $Ax=b$ by using partial pivoting.

b$.$ Solve the system $Ax=b$ by using LU decomposition.

c$.$ Find a solution of the system $Ax=b$ with $x_0={\left[\begin{array}{ccc}0& 0& 0\end{array}\right]}^T$ by using Jacobi Method with ${10}^{-4}$ accuracy.

d$.$ Find a solution of the system $Ax=b$ with $x_0={\left[\begin{array}{ccc}0& 0& 0\end{array}\right]}^T$ by using Gauss$-$Siedel Method with ${10}^{-4}$ accuracy.