**Gauss Elimination**

Solve the following set using Gauss elimination

-x + y + 2z = 2

3x – y + z = 6

-x+3y+4z =4

**• Solution**

The solution proceeds as follows:

1. Equation (6.1-1) is the pivot equation. Multiply it by -I and add the result to (6.1-3) to obtain 2y + 2z = 2, which is equivatenr to y + z = I. Next multiply

(6.1-1) by 3 and add the result to (6.1-2) to obtain 2y + Tz = 12.Thuswe have a new set of two equations in two unknowns:

2. Equation (6.1-4) is the new pivot equation. Multiply it by -2 and add the result to (r-:5).to obtain 5z = 10, or: = 2. Substitute this value into (6.1-4) to obtain y -+ 2b I, or y = -1. Then substitute the values of y and z into (6.1-1) to obtain

r’xl·1 + 4 = 2, or x = 1.

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