Question

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`?

Answer 1

`(x_1,x_2,x_3)=(1,1,1)`

Explanation:

Initial Augmented Matrix:
`color(white)("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) )`