Solve the following equations by Gauss-Seidel method by taking two iterations. \(28x+4y-z=32,\ 2x+17y+4z=35,\ x+3y+10z=24\).

Diagonally dominant. \(x=\frac1{28}(32-4y+z),\ y=\frac1{17}(35-2x-4z),\ z=\frac1{10}(24-x-3y)\). Start \(y=z=0\), using latest values.

Iteration 1: \(x_1=\frac{32}{28}=1.1429\); \(y_1=\frac{35-2.2857}{17}=1.9244\); \(z_1=\frac{24-1.1429-5.7731}{10}=1.7084\)

Iteration 2: \(x_2=\frac{32-7.6975+1.7084}{28}=0.9290\); \(y_2=\frac{35-1.8579-6.8336}{17}=1.5476\); \(z_2=\frac{24-0.9290-4.6428}{10}=1.8428\)

After two iterations: \(x\approx0.9290,\ y\approx1.5476,\ z\approx1.8428\) (exact solution \(x\approx0.9936,\ y\approx1.5070,\ z\approx1.8485\)).