Linear System Gauß Algorithm in CAS
Algorithm assumes diagonal element not equal to zero!
| COM1 | Transfer LGS (linear system) into a matrix: |
| COM2 | Access matrix row: Element(Ab,z) -- Matrix element: Element(Ab,z,s) \\ Add abbreviated CAS functions that are easier to read\\\ add 1st row to rows 2,3,4 - row z == A_b'(z) , element z,s == A_b(z,s) |
| COM21 | Adapt static Gaussian step to version that dynamically accesses matrix elements:\\ dynamic \to Changes to the LGS are correctly implemented in the Gaussian steps! |
| COM3 | add 2nd row to rows 3 and 4 \to L2 Gaussian step from elementary matrices |
| COM4 | A4 - add 3rd row to row 4 \and A5 divide by diagonal elements \to diag(1,1,1,1) |
| COM5 | Back substitution with elementary matrices \\ - A6: Line 4 to lines 3,2,1 - A7: Line 3 to line 2 - RRef: Line 2 to line 1 |
| COM6 | Gaussian step made up of elementary matrices |
| COM7 | RowEchelonForm: ReducedRowEchelonForm( )_{command} \\ Read the solution IL from column 5 and verify the result A IL = b |