Word Count : 672

---

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. _________ ________ ________ _______ __________.
_________ _______ ___ _______ ______ ____ __________ _____ ________ ____.
____ ________ __________ ___ _______ ______ ___ ___.
_____ __________ _________ __________ _______ ________ ________ ________ _____ ______.
______ ________ ___ ________ ___ ______ _________ _____ __________ ________.
_______ _________ ________ __________ _____ __________ ______ __________ ______ _____ _______.
________ __________ ________ _______ ______ _______ __________ _______ _____.
____ ________ ___ ____ ________ ________ _______ __________.
______ _____ ___ __________ ______ ___.
____ ________ __________ ________ ___ _____ __________ ______ _________ ________ _______ _______.
_________ ____ ______ ________ ______ _____ ______ ______ _______ ____ _____.
__________ __________ __________ __________ __________ ____ ___ ____ ____ ______ _______.
___ _________ _________ _________ ________ _______.
_______ ______ ______ _______ ________ ____ ________ _________ ___ ____.
________ _______ __________ _______ _________ _______ _______.
_______ ________ ________ ________ _________ ___ ________.
__________ ______ ______ ________ ___.
_____ _______ _______ _________ _______ _______ _______ ______.
_________ ______ ___ ____ ______ ______.
___ _________ ______ ______ _______ ______ _____ _____.
_________ _______ ________ ______ ________ ______ ________.
_______ ______ ______ ______ ____ ____ ____ __________ ___ ________ ______.
__________ _______ ___ ________ _____ _____ _________ _________ ________.
__________ ___ ___ _____ _____ _____ ____ _____.
________ _____ _________ _______ _____.
__________ _______ ____ _____ _______ ______ ______ _______.
_________ ____ ______ ___ _________ ___ ____ _________ __________.
______ ___ ______ ________ _____ ________ _______ _______.
____ _____ _______ ______ ________ __________ _________ ________ _______ ___.
_____ ____ _________ __________ ________ ___.
__________ _______ ___ ______ _______ __________ ___ ___ ______ ____ _____.
______ _________ __________ _____ _________ _____.
_______ ____ __________ _____ ______ __________ ________ ____.
___ ________ ________ __________ _________ _________.
______ _______ __________ ____ __________ ______ ___ __________ ______.
______ ___ _________ ____ _______ ______ __________ ___ _________.
______ ______ _________ ________ __________ ______.
____ ___ _____ _______ _____ ___ ___ ___ ____ ________ _______ ____.
_______ ____ _____ _______ ________ ________ ______ _________.
_____ ____ ___ __________ _______ ___ _________ ________.
_____ _______ _____ _______ ________ ______ ___ _________.
________ _______ ___ ___ ______ ___ ________.
__________ ________ _________ _________ _______ _______.
________ ________ ____ _________ _______ ________.
_______ _____ _______ ____ ________ ________ __________ ________.
_________ ______ _____ ______ _______ _______ __________ _________.
_______ ___ _________ _________ ________ _________ ___ _________ _______ _______.
______ ________ ________ _________ ________ __________.
__________ ___ ________ ________ ___ _____ _____ ____ ____ ____.
_________ _____ ____ _____ ___ __________ __________.
_______ __________ ________ _______ ________ ______ ______ _________ ________ _________ _______.
____ _____ _____ ___ _____ ______.
________ ___ _______ __________ ____ __________.
______ _________ ______ ________ _____ ___ _____ _______ ________ _________ _______ _______.
______ _______ ___ _____ ___ _______ _____.
__________ _____ _________ _________ ________ ___ _______ _________.
____ ________ ________ __________ _____ _________ ______ ____ _____.
____ _____ _____ ___ ____ ______ _________.
_____ __________ ______ ____ __________ ______.
____ ______ __________ __________ ___ __________ _______ ___.
_________ ______ _____ ____ ____ _____ ___ ___ ___.
_________ ____ ___ ______ _______ _____ __________ __________ ________ _____.
__________ ________ ___ _________ _____ ______ ___.
_________ __________ ______ _______ ______ _______ ________.
______ __________ ______ __________ _____ ______ ____ __________ _____.
____ __________ _______ ____ ____ _____ _________ _________.
Get Full Answer on WhatsApp