$10x_1+2x_2-x_3=27$

$-3x_1-5x_2+2x_3=-61\mathrm{.}5$

$x_1+x_2+6x_3=-21\mathrm{.}5$

$($a$)$ Solve the equation using pure Gaussian elimination. Show the entire calculation process

$($b$)$ Verify the solution by substituting it into the original equation.

$($c$)$ MATLAB code