Question

How do you solve `-5x+6y-z= -26` and `x-4y-4z= -27` and `6x+y+z = 38` using matrices?

Answer 1

`[(1+0+0 |+5),(0+1+0|+1),(0+0+1|+7)]`

`x=5; y=1; z=7`

Explanation:

AS a check

`"Target values"->x=5; y=1; z=7`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(red)("These can go wrong very easily. Particularly if fractions are involved.")`

`" "x" "y" "z" " =`
`[(-5+6-1 |-26),(1-4-4|-27),(6+1+1|38)]`
`Row1 -:(-5)" and "Row3-:6`
`color(red)(" "darr)`

`[(1-6/5+1/5 |+26/5),(1-4-4|-27),(1+1/6+1/6|19/3)]`
`Row2-Row1`
`color(red)(" "darr)`

`[(1-6/5+1/5 |+26/5),(0-14/5-21/5|-161/5),(1+1/6+1/6|19/3)]`
`Row2xx(-5/14)`
`color(red)(" "darr)`

`[(1-6/5+1/5 |+26/5),(0+1+3/2|+23/2),(1+1/6+1/6|19/3)]`
`Row1+6/5Row2`
`color(red)(" "darr)`

`[(1+0+2 |+19),(0+1+3/2|+23/2),(1+1/6+1/6|19/3)]`
`Row3-Row1`
`color(red)(" "darr)`

`[(1+0+2 |+19),(0+1+3/2|+23/2),(0+1/6-11/6|-38/3)]`
`Row3xx6`
`color(red)(" "darr)`

`[(1+0+2 |+19),(0+1+3/2|+23/2),(0+1-11|-76)]`
`Row3-Row2`
`color(red)(" "darr)`

`[(1+0+2 |+19),(0+1+3/2|+23/2),(0+0-25/2|-175/2)]`
`Row3xx(-2/25)`
`color(red)(" "darr)`

`[(1+0+2 |+19),(0+1+3/2|+23/2),(0+0+1|+7)]`
`Row1-2Row3" and "Row2-3/2Row3`
`color(red)(" "darr)`

`[(1+0+0 |+5),(0+1+0|+1),(0+0+1|+7)]`