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  3. 1 consider the following system of equations 3x1 x2 1...

Question: 1 consider the following system of equations 3x1 x2 1...

Question details
1. Consider the following system of equations:
3x1 +x2 =1
x1 –5x2 =11
(a) Solvethegivensystemusingthegraphicalmethod(usingMATLABforplotting).
(b) ExpresseveryequationasananonymousMATLABfunction.
(c) With MATLAB, use the functions in (b) to verify your solution in (a).


2. Consider the following system of equations:
2x2 + 5x3 = 1
2x1+x2+ x3=1 3x1 + x2 = 2
(a) SolveusingCramer’srule.
(b) SolveusingGausseliminationwithpartialpivoting.
Show all steps of computation.


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.
(b) Show the result of running your function on the following system of equations with tol =
0.00001
2x2 + 5x3 = 1 2x1+x2 +x3=1 4x1 +2x2 +2x3 =4
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