# How do you solve using gaussian elimination or gauss-jordan elimination, x_1+x_2+x_3=3, x_1+2x_2-x_3=2, 2x_1+x_2+2x_3=5?

Nov 7, 2016

$\left({x}_{1} , {x}_{2} , {x}_{3}\right) = \left(1 , 1 , 1\right)$

#### Explanation:

Initial Augmented Matrix:
$\textcolor{w h i t e}{\text{XXXXXX")x_1color(white)("XXXXXX")x_2color(white)("XXXXX}} {x}_{3}$
( (color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")3), (color(white)("XXXXX")1,color(white)("XXXXX")2,color(white)("XXXX")-1,color(white)("XXXXX")2), (color(white)("XXXXX")2,color(white)("XXXXX")1,color(white)("XXXXX")2,color(white)("XXXXX")5) )

Pivot Row: 1 Pivot Column: 1
pivot Row reduced:
( (color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")3), (color(white)("XXXXX")1,color(white)("XXXXX")2,color(white)("XXXX")-1,color(white)("XXXXX")2), (color(white)("XXXXX")2,color(white)("XXXXX")1,color(white)("XXXXX")2,color(white)("XXXXX")5) )

Non-pivot rows reduced for pivot column
( (color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")3), (color(white)("XXXXX")0,color(white)("XXXXX")1,color(white)("XXXX")-2,color(white)("XXXX")-1), (color(white)("XXXXX")0,color(white)("XXXX")-1,color(white)("XXXXX")0,color(white)("XXXX")-1) )

Pivot Row: 2 Pivot Column: 2
pivot Row reduced:
( (color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")1,color(white)("XXXXX")3), (color(white)("XXXXX")0,color(white)("XXXXX")1,color(white)("XXXX")-2,color(white)("XXXX")-1), (color(white)("XXXXX")0,color(white)("XXXX")-1,color(white)("XXXXX")0,color(white)("XXXX")-1) )

Non-pivot rows reduced for pivot column
( (color(white)("XXXXX")1,color(white)("XXXXX")0,color(white)("XXXXX")3,color(white)("XXXXX")4), (color(white)("XXXXX")0,color(white)("XXXXX")1,color(white)("XXXX")-2,color(white)("XXXX")-1), (color(white)("XXXXX")0,color(white)("XXXXX")0,color(white)("XXXX")-2,color(white)("XXXX")-2) )

Pivot Row: 3 Pivot Column: 3
pivot Row reduced:
( (color(white)("XXXXX")1,color(white)("XXXXX")0,color(white)("XXXXX")3,color(white)("XXXXX")4), (color(white)("XXXXX")0,color(white)("XXXXX")1,color(white)("XXXX")-2,color(white)("XXXX")-1), (color(white)("XXXXX")0,color(white)("XXXXX")0,color(white)("XXXXX")1,color(white)("XXXXX")1) )

Non-pivot rows reduced for pivot column
( (color(white)("XXXXX")1,color(white)("XXXXX")0,color(white)("XXXXX")0,color(white)("XXXXX")1), (color(white)("XXXXX")0,color(white)("XXXXX")1,color(white)("XXXXX")0,color(white)("XXXXX")1), (color(white)("XXXXX")0,color(white)("XXXXX")0,color(white)("XXXXX")1,color(white)("XXXXX")1) )