Solve \(10x+y+z=12,\ x+10y+z=12,\ x+y+10z=12\) using the Gauss-Jacobi's method by taking two iterations.

Q.1 (f) Solve \(10x+y+z=12,\ x+10y+z=12,\ x+y+10z=12\) using the Gauss-Jacobi's method by taking two iterations.

Doubtly Asked 25 Oct 2026 mu engineering Save WhatsApp Report

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Diagonally dominant. \(x=\frac{12-y-z}{10},\ y=\frac{12-x-z}{10},\ z=\frac{12-x-y}{10}\). Start \(x_0=y_0=z_0=0\).

Iteration 1: \(x_1=y_1=z_1=\frac{12}{10}=1.2\)

Iteration 2: \(x_2=\frac{12-1.2-1.2}{10}=0.96,\ y_2=0.96,\ z_2=0.96\)

After two iterations \(x=y=z=0.96\) (exact solution \(x=y=z=1\)).

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report

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