Numerical Methods20785 marksNumerical: Gauss elimination pivotingGaussian elimination with partial pivoting
Solve the following system of linear equation by Gauss Elimination with Pivoting 2x + 2y + z = 6, 4x + 2y + 3z = 4, x - y + 1 = 0.
Solve the following system of linear equation by Gauss Elimination with Pivoting $2x + 2y + z = 6$, $4x + 2y + 3z = 4$, $x - y + 1 = 0$. [5]
Equations: - $2x + 2y + z = 6$ - $4x + 2y + 3z = 4$ - $x - y + 1 = 0 \Rightarrow x - y = -1$ Augmented matrix: $$[Ab] = \begin{bmatrix} 2 & 2 & 1 & & 6 \ 4 & 2 & 3 & & 4 \ 1 & -1 & 0 & & -1 \end{bmatrix}$$ Largest magnitude in column 1: $4 2 1$. Swap $R1 \leftrightarrow R2$: $$\begin{bmatrix} 4...