Question

How do you solve using gaussian elimination or gauss-jordan elimination, `-2x -5y +5z =4`, `-3x -y -z =10`, `5x +3y -z =10`?

Answer 1

`P="[(43,-46,-28)]"`

Explanation:

`([-2,-5,5,|,4],[-3,-1,-1,|,10],[5,3,-1,|,10])`
`R_1=R_1xx5`
`R_2=R_2xx5`
`R_3=R_3xx3`

`([-10,-25,25,|,20],[-15,-5,-5,|,50],[15,9,-3,|,30])`
`R_2=R_2+R_3`
`R_3=R_3xx2/3`

`([-10,-25,25,|,20],[0,4,-8,|,80],[10,6,-2,|,20])`
`R_3=R_3+R_1`
`R_1=R_1xx1/5`
`R_2=R_2xx1/4`

`([-2,-5,5,|,4],[0,1,-2,|,20],[0,-19,23,|,40])`
`R_3=R_3+19xxR_2`

`([-2,-5,5,|,4],[0,1,-2,|,20],[0,0,-15,|,40+20xx19])`
`R_3=R_3xx-1/15`

`([-2,-5,5,|,4],[0,1,-2,|,20],[0,0,1,|,-(cancel5xx8+cancel5xx4xx19)/(cancel5xx3)])`
`R_2=R_2+2xxR_3`

`([-2,-5,5,|,4],[0,1,0,|,20-2xx(4xx(2+19))/(3)],[0,0,1,|,-(4xx(2+19))/(3)])`
Simplifing right side

`([-2,-5,5,|,4],[0,1,0,|,(60-2xx84)/3],[0,0,1,|,-84/3])`
`R_1=R_1+5xxR_2`
`R_1=R_1-5xxR_3`
`R_1=R_1xx-1/2`

`([1,0,0,|,-2+5xx(60-198)/-6-5xx(-84/-6)],[0,1,0,|,(60-198)/3],[0,0,1,|,-28])`
Simplifing right side

`([1,0,0,|,-2+5xx6xx(10-33)/-6-5xx6xx(14/6)],[0,1,0,|,(60-198)/3],[0,0,1,|,-28])`

`color(red)x=-2-5xx(10-33)-5xx14=-2+115-70color(red)(=43)`

`color(red)y=(60-198)/3=20-66color(red)(=-46)`

`color(red)(z=-28)`

`P="[(43,-46,-28)]"`