Word Count : 672

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We are given the system of equations: $$ \begin{aligned} (1)\quad &2x_1 + 3x_2 + 4x_3 + x_4 = 3 \\ (2)\quad &x_1 + 2x_2 + 0x_3 + x_4 = 2 \\ (3)\quad &2x_1 + 3x_2 + x_3 - x_4 = 1 \\ (4)\quad &x_1 - 2x_2 - x_3 + 4x_4 = 5 \end{aligned} $$ We solve this using Gauss Elimination with partial pivoting. --- ### Step 1: Write the augmented matrix $$ \begin{bmatrix} 2 & 3 & 4 & 1 & | & 3 \\ 1 & 2 & 0 & 1 & | & 2 \\ 2 & 3 & 1 & -1 & | & 1 \\ 1 & -2 & -1 & 4 & | & 5 \\ \end{bmatrix} $$ --- ### Step 2: Pivoting (Row Exchange) Look at column 1. _____ _______ ________ __________ ___ ____ ______ _________.
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