How do you solve using gaussian elimination or gauss-jordan elimination, #X- 3Y + 2Z = -5#, #4X - 11Y + 4Z = -7#, #3X - 8Y + 2Z = -2#?

1 Answer
Sep 26, 2017

Answer:

The solution is #((X),(Y),(Z))=((34+10Z),(13+4Z),(Z))#

Explanation:

Perform the gauss-jordan elimination on the augmented matrix

#((1,-3,2,|,-5),(4,-11,4,|,-7),(3,-8,2,|,-2))#

We perform the following operations on the rows

#R2larrR2-4R1# and #R3larrR3-3R1#

#((1,-3,2,|,-5),(0,1,-4,|,13),(0,1,-4,|,13))#

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

#((1,0,-10,|,34),(0,1,-4,|,13),(0,0,0,|,0))#

The solution is

#((X),(Y),(Z))=((34+10Z),(13+4Z),(Z))#