HAND CALCULATION: Use the Gauss-Seidel iterative technique to find approximate solutions to 10x1 X 2 + 2x3 = 91 - X1 + 11x2 – X3 + 3x4 = 25 2x1 – X2 + 10x3 - X4 = -11 3x2 – X3 + 8x4 = 15 starting with zeroth iteration 22 = 0 23 = 0 24 = 0 until the first iteration. What is 23 after the first iteration? Type your answer...

We use the Gauss-Seidel iterative technique to solve the system of equations. We isolate x2 in the second equation and substitute the zeroth iteration values, giving us x2 ≈ 2.27 after the first iteration.

The Gauss-Seidel iterative technique.

In this method, we approximate the solutions to the system by iteratively solving each equation for a specific variable, then substituting the values obtained from the other equations.

We start with an initial guess for each variable, in this case they are all zeros, and then iteratively improve upon this guess.

The second equation would be solved for x2, giving us x2 = (25 + x1 - x3 - 3x4)/11.

Given that x1, x3, and x4 are all zero in the zeroth iteration,

this simplifies to x2 = 25/11 ≈ 2.27 after the first iteration.

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