Linear Systems. Write a separate m$-$file for each part. Remember to capture Matlab$$s screen output to a diary file.

$($a$)$ Solve the following system using MATLAB$$s blackslash $\backslash$ operator.

$($b$)$ Let the matrix A be given by

$121$x$12312$ x$2=8.$

$223$x$39$

$17241815$

$23571416$ A$=46132022.$

$10121921311182529$

Solve the system Ax $=$ b for the following right hand side vectors b using Matlab$$s backslash operator.

$244$

$1$ b$2=4,$

$2114$

$($c$)$ In part $($b$),$ since we have the same coefficient matrix for three linear systems, one does not need to do three separate linear solves; in such cases it is possible to solve all three systems simultaneously by defining a matrix B $=[$b$1,$ b$2,$ b$3]$ which has b$1,$ b$2,$ and b$3$ as its columns. Next, one can solve the matrix equation AX $=$ B using X $=$ A $\backslash$ B$.$ Then, the matrix X will contain the solutions to the systems Axi $=$ bi$,$ i $=1,...,3$ as its columns, X $=[$x$1,$ x$2,$ x$3].$ Redo part $($b$)$ using this technique.