How do you solve using gaussian elimination or gauss-jordan elimination, #3x – y + 2z = 6#, #-x + y = 2#, #x – 2z = -5#?

1 Answer
Jul 16, 2016

Answer:

#color(red)(x=1,y=3,z=3)#

Explanation:

Initial Augmented Matrix:

#[ ( 3, -1, 2, 6), ( -1, 1, 0, 2), ( 1, 0, -2, -5) ]#

Adding Row-2 and Row-3 to Row-1

#[ ( 3, 0, 0, 3), ( -1, 1, 0, 2), ( 1, 0, -2, -5) ]#

Dividing Row-1 by 3

#[ ( 1, 0, 0, 1), ( -1, 1, 0, 2), ( 1, 0, -2, -5) ]#

Adding Row-1 to Row-2

#[ ( 1, 0, 0, 1), ( 0, 1, 0, 3), ( 1, 0, -2, -5) ]#

Adding Row-1 from Row-3

#[ ( 1, 0, 0, 1), ( 0, 1, 0, 3), ( 0, 0, -2, -6) ]#

Dividing Row-3 by -2

#[ ( 1, 0, 0, 1), ( 0, 1, 0, 3), ( 0, 0, 1, 3) ]#

Obviously

#color(red)(x=1,y=3,z=3)#