Develop an M$-$file function based on the following figure to implement Gauss$-$elimination with partial pivoting $.$ Modify the function so that it computes and returns the determinant $($ with the correct sign $),$ and detects wether wether the system is singular based on a $$near$-$zero" as being when the absolute value of the determinant is below a tolerance $.$ When this occurs $,$ design the function so that an error message is displayed and the function terminates $.$ Here is the function first line :

function $[$x$,$D$]=$ GaussPivotNew$($A$,$b$,$tol$)$

where D $=$ the determinant and tol $=$ the tolerance $.$