Question

How do you solve using gaussian elimination or gauss-jordan elimination, `2x-3y+z=1`, `x-2y+3z=2`, `3x-4y-z=1`?

Answer 1

The given set of equations is inconsistent; there is no solution

Explanation:

Given the equations (re-ordered so first equation has a coefficient of `1` for `x`
`color(white)("XX"){(x-2y+3=2),(2x-3y+z=1),(3x-4y-z=1):}color(white)("XXX"){:([1]),([2]),([3]):}`

Subtracting `2xx`[1] from equation [2]
and `3xx`[1] from equation [3]
`color(white)("XX"){(x-2y+3=2),(0x+1y-5z=-3),(0x+2y-10z=-5):}color(white)("XXX"){:([1]),([4]),([5]):}`

Subtracting `2xx`[4] from equation [5]
`color(white)("XX"){(x-2y+3=2),(0x+1y-5z=-3),(0x+0y+0z=1):}color(white)("XXX"){:([1]),([4]),([6]):}`

Since [6] is impossible
`color(white)("XXX")`the given equations are inconsistent.