3. Consider the MATLAB function GaussPivot() given in class in slide 5-31.

(a) Modify GaussPivot() so that it computes and returns the determinant (with the correct sign) and

detects whether the system is singular based on a near-zero determinant. Define near-zero as

being when the absolute value of the determinant is below a tolerance. When this occurs, the

function should display an error message and terminate. The first line of the function should be:

function [x, D] = GaussPivot2(A, b, tol) where D is the determinant, and tol is the tolerance. Do not use the Matlab det() function.

(b) Showtheresultofrunningyourfunctiononthefollowingsystemofequationswithtol=0.00001

2x2 + 5x3 = 1

2x1+x2 +x3=1 4x1 +2x2 +2x3 =4

function x Gausts Pivot (A,b) t GaussPivot: Gauss elimination pivoting tx Gausspivot lA.b) Gauss elinination with pivoting. t input: Acoefficient matrix b right hand side vector s output: tx solution vector Im, nl-size(A): if m-n, error ('Matrix A must be square'): end nb-n+1 Aug" [A b); t forvard elimination for k- 1:n-1 oue partial pivo ting big, il-max (abs (Aug (k:n,x)) ipr-irk-1, end tor i -k+lin factor Aug (i,k)/Aug (k,k)i end end 3 back substitution xszeros (n. 1)a x(n) Aug (n,nb)/Aug (n,n) i for i n-1:-1:1 end eterminant Evaluation lon matrix can be simply