How do you solve using gaussian elimination or gauss-jordan elimination, #y+z=-3#, #x-y+z=-7#, #x+y=2#?

1 Answer
Mar 28, 2017

Answer:

#x =0, y =2 and z =-5#

Explanation:

#r_1 -># #0#........#1#........#1#........#-3#
#r_2 -># #1#....#-1#........#1#........#-7#
#r_3 -># #1#........#1#........#0#............#2#

#r_1 = r_1 + r_2#
#1#........#0#........#2#........#-10#
#1#....#-1#........#1#........#-7#
#1#........#1#........#0#............#2#

#r_2 = r_1 - r_2#
#1#........#0#........#2#........#-10#
#0#........#1#........#1#........#-3#
#1#........#1#........#0#............#2#

#r_3 = r_3 - r_1#
#1#........#0#........#2#........#-10#
#0#........#1#........#1#........#-3#
#0#........#1#....#-2#...........#12#

#r_3 = r_3 - r_2#
#1#........#0#........#2#........#-10#
#0#........#1#........#1#........#-3#
#0#........#0#....#-3#...........#15#

#r_3 = r_3/-3#
#1#........#0#........#2#........#-10#
#0#........#1#........#1#........#-3#
#0#........#0#........#1#........#-5#

#r_2 = r_2 - r_3#
#1#........#0#........#2#........#-10#
#0#........#1#........#0#............#2#
#0#........#0#........#1#........#-5#

#r_1 = r_1 - 2r_3#
#1#........#0#........#0#...........#0#
#0#........#1#........#0#............#2#
#0#........#0#........#1#........#-5#