Q$1$

$(10$ pts$)$ Given the equations

$5x_1+1x_2-0\mathrm{.}5x_3=13\mathrm{.}5$

$-6x_1-12x_2+4x_3=-123$

$2x_1+2x_2+10x_3=-43$

$($a$)$ Solve by hand using Gauss Elimination. Show all steps of the calculation.

$($b$)$ Substitute your results in to the original equations to check your answers.

$($c$)$ Write a Gauss Elimination code and solve the problem. Verify your implementation.

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

Pivoting and scaling are both optional. Solve it by hand then write the code in MATLAB