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Find approximate solutions of the following system using Gauss Elimination with partial pivoting. Use 4 significant digits in all process. Apply rounding if you need. Calculate absolute and relative errors for each solutions.
\begin{align} 9x_1 + x_2 + 2x_3 − 5x_4 &=37 \\ 4 x_2 − 3 x_3 + x_4 &= 2 \\ −3 x_1 + 4 x_2 − 2 x_4 &=8\\ 2 x_1 − 3 x_2 + 5 x_3 + x_4 &=0 \end{align}
Exact Solution: $x_1 = 2, x_2 = 2, x_3 = 1, x_4 = −3$