How do you solve using gaussian elimination or gauss-jordan elimination, x+y+z=1, 3x+y-3z=5 and x-2y-5z=10?

1 Answer
Feb 13, 2016

((x),(y),(z)) = ((6),(-7),(2))

Explanation:

The linear equation:
x+y+z =1
3x+y-3z=5
x-2y-5z=10
can be written in Matrix form as:
(x, y, z)((1,1,1),(3,1,-3),(1,-2,-5)) = ((1), (5), (10))
Let's now use gauss elimination:
((1,1,1, |, 1),(3,1,-3, |, 5),(1,-2,-5, |, 10))

color(red)(R_2=-3R_1+R_2) ((1,1,1,|, 1),(0,-2,-6,|, 2),(1,-2,-5, |, 10))

color(red)(R_3 =-R_1+R_3) ((1,1,1,|, 1),(0,-2,-6,|, 2),(0,-3,-6, |, 9))

color(red)(R_3 =-3/2R_2+R_3) ((1,1,1,|, 1),(0,-2,-6,|, 2),(0,0,3, |, 6))
Now what we have is:
x+y+z= 1 --------------------------------------------------------- (1)
" " -2y-6z = 2 ---------------------------------------------------------(2)
" " 3z = 6 ; z= 2 substitute this into (2) above solve for y
y = -7 sub for y and z into (1) x= 6