$(1)$ Apply Gaussian Elimination with partial pivoting to solve the following system, and check if the calculated numbers satisfy the equations.

$-3x_1+2x_2+6x_3=4$

$10x_1-7x_2=7$

$5x_1-x_2+5x_3=6$

$(2)$ Read and understand the Matlab script file for Gaussian elimination with partial pivoting below and use the Matlab function to solve the system in $(1).$ read the question from the picture please.