Find the complete solution of the system
{x−y+z=2x+y+3z=62y+3z=5
using Gaussian Elimination.
For this system we have
[1−11211360235]
R2−R1→R2
[1−11202240235]
12R2
[1−11201120235]
R3−2R2→R3
[1−11201120011]
Now we have equivalent matrix in row-echelon form and the corresponding system is
{x−y+z=2y+z=2z=1
Then we back-substitute z=1 into the second equation and solve for y
y+1=2Back-substitute z=1y=1Subtract 1
Now we back-substitute y=1 and z=1 into the first equation and solve for x
x−1+1=2Back-substitute y=1 and z=1x=2Simplify
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