How do you solve using gaussian elimination or gauss-jordan elimination, #2x-3y-z=2#, #-x+2y-5z=-13#, #5x-y-z=-5#?

1 Answer
Dec 17, 2017

Answer:

Taken you almost to the end. I will let you finish it off.
Check my working!!!

Explanation:

#color(green)([(2,-3,-1,|,2),(-1,2,-5,|,-13),(5,-1,-1,|,-50)])#

#R_1-:2 color(white)("ddd")R_3-:5#
# color(white)("dddddd")darr #

#color(green)([(1,-3/2,-1/2,|,1),(-1,2,-5,|,-13),(1,-1/5,-1/5,|,-10)])#

#R_1+R_2 color(white)("ddd")R_3+R_2#
# color(white)("dddddd")darr #

#color(green)([(0,1/2,-11/2,|,1),(-1,2,-5,|,-13),(0,9/5,-26/5,|,-10)])#

#R_1xx2 color(white)("ddd")R_3xx5#
# color(white)("dddddd")darr #

#color(green)([(0,1,-11,|,2),(-1,2,-5,|,-13),(0,9,-26,|,-50)])#

#R_2-2R_1 color(white)("ddd")R_3-9R_1#
# color(white)("dddddddd")darr #

#color(green)([(0,1,-11,|,2),(-1,0,-27,|,-17),(0,0,-125,|,-68)])#

#R_2-:(-1)color(white)("ddd")R_3-:(-125) #
# color(white)("dddddddd")darr #

#color(green)([(0,1,-11,|,2),(1,0,27,|,17),(0,0,1,|,+68/125)])#

You should be able to finish this now.

PLEASE MAKE SURE THERE ARE NO MISTAKES. Not checked!