Q$2$

$(10$ pts$.)$ Solve the following system of equations by LU decomposition:

$8x_1+4x_2-x_3=11$

$-2x_1+5x_2+x_3=4$

$2x_1-x_2+6x_3=7$

a$)$ by hand

b$)$ using a python or matlab script that you write.

NOTE: Your code should be general enough to handle an n$-$by$-$n system for any $n.$

Pivoting and scaling are both optional.

c$)$ Make a statement about verification based on the results of $($a$)$ and $($b$).$Solve it by hand then write the code in MATLAB