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

1 Answer
Apr 6, 2016

Answer:

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.