How do you solve using gaussian elimination or gauss-jordan elimination, #x+y+z=2#, #2x-3y+z=-11#, #-x+2y-z=8#?

1 Answer
Jun 1, 2018

Answer:

The solution is #((x),(y),(z))=((1/3),(10/3),(-5/3))#

Explanation:

The augmented matrix is

#A=((1,1,1,|,2),(2,-3,1,|,-11),(-1,2,-1,|,8))#

The pivot is in the the first column of the first row

Perform the operations on the rows

#R2larrR2-2R1# and #R3larrR3+R1#

#=>#, #((1,1,1,|,2),(0,-5,-1,|,-15),(0,3,0,|,10))#

Make the pivot in the second column

#R2larr(R2)/(-5)#

#=>#, #((1,1,1,|,2),(0,1,1/5,|,3),(0,3,0,|,10))#

Eliminate the second column

#R1larrR1-R2# and #R3larrR3-3R2#

#=>#, #((1,0,4/5,|,-1),(0,1,1/5,|,3),(0,0,-3/5,|,1))#

Make the pivot in the third column

#R3larr(R3xx-5/3)#

#=>#, #((1,0,4/5,|,-1),(0,1,1/5,|,3),(0,0,1,|,-5/3))#

Eliminate the third column

#R1larr(R1-4/5xxR3)# and #R2larr(R2-1/5xxR3)#

#=>#, #((1,0,0,|,1/3),(0,1,0,|,10/3),(0,0,1,|,-5/3))#

The solution is

#((x),(y),(z))=((1/3),(10/3),(-5/3))#