Computing Determinants Using Gaussian Elimination IT Assignment Help

Assignment Task

Task

Here the forward phase of elimination is used to compute the determinant of an   matrix.

Gaussian elimination is the key algorithm for most of Linear Algebra.  
The assignment is to modify the function 
obtain a function that returns two values:   
(1)  the sign difference between the determinant of the  input matrix and the determinant of the row echelon form produced by the forward phase of elimination and (2) the product of the diagonal elements diagonal elements of the row echelon matrix produced by the  forward phase of elimination.    
The principles used in this assignment are the following:
1. The forward phase of elimination uses only two kinds of row operations:   replacement and interchange.
2. Replacement operations leave the determinate unchanged.
3. Interchange operations reverse the sign of the determinant.
4. The determinate of an   row echelon matrix is the product of its diagonal elements.Hence, the forward phase of the elimination produces a row echelon matrix with an easily computed  determinant that is the same as the original matrix except for a possible change of sign. Monitoring,  interchange operations determines any change in sign.
Steps:
Step 1:  Change the function declaration to return two values (1) sign--the difference in the sign of the  determinant between the original matrix and the row echelon matrix and (2) diag_prod--the determinant of the row echelon matrix, i.e. product of the diagonal elements.Step 2:  Determine the cumulative sign change due to interchange operations used in the forward phase of  elimination.    
A simple way to make this determination is to (1) initialize a variable sign to one (sign = 1;)  

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