Find the complete solution of the system
{3x+y=2−4x+3y+z=42x+5y+z=0
We transform the system into row-echelon form
[3102−43142510]
13R1
[113023−43142510]
R2+4R1→R2
[113023013312032510]
R3−2R1→R3
[1130230133120301331−43]
313R2
[11302301313201301331−43]
R3−133R2→R3
[113023013132013000−8]
−18R3
[1130230131320130001]
This last matrix is in row-echelon form, so we stop the Gaussian Elimination Process. Now if we translate the last row back into equation form, we get 0x+0y+0z=1 or 0=1, which is false. This means that the system has no solution or it is inconsistent.
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