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