Question

How do you solve using gaussian elimination or gauss-jordan elimination, `2x₁+4x₂-6x₃= 10`, `3x₁+3x₂-3x₃= 6`?

Answer 1

`P=({-1-p, 3+2p, p}, p in RR)`

Explanation:

`([2,4,-6,|,10],[3,3,-3,|,6])~~([6,12,-18,|,30],[6,6,-6,|,12])`
`R_1=R_1xx3`
`R_2=R_2xx2`
`R_2=R_2-R_1`

`([6,12,-18,|,30],[0,-6,12,|,-18])~~([1,2,-3,|,5],[0,1,-2,|,3])`
`R_1=R_1xx1/6`
`R_2=R_2xx-1/6`
`R_1=R_1-2xxR_2`

`([1,0,1,|,-1],[0,1,-2,|,3])`

We have to set `x_3` as parameter `p`:
`x_1=-1-p`
`x_2=3+2p`
`x_3=pcolor(white)(QQQQQQQQQQQ)p in RR`

`P=({-1-p, 3+2p, p}, p in RR)`