# Solve in c applying the Gauss method, the system of equations: -x+4y-7z=5 x-y-2z=-2 2y-6z=2

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First we create the augmented matrix with the coefficients:

`[(-1,4,-7,|,5),(1,-1,-2,|,2),(0,2,-6,|,2)]` Now we row reduce:

`=>[(1,-4,7,|,-5),(0,3,-9,|,7),(0,2,-6,|,2)]` R1*(-1);R1+R2;R3

`=>[(1,-4,7,|,-5),(0,1,-3,|,7/3),(0,0,0,|,4)]` R1;1/3R2;-3/2R3+R2

Since the bottom row has all zeros in the coefficient slots there are no solutions. (The bottom constraints are parallel planes)

System hasn't solutions for:

`det [[-1,4,-7],[1,-1,-2],[0,2,-6]]=0`

Columns are dipendent, indeed, if set a system for the first two columns:

`-lambda_1+4lambda_2=-7`

`lambda_1-lambda_2=-2`

That has solution: `lambda_1=-5` `lambda_2=-3`

If we apply that ones at the third row:

`0 xx lambda_1 + 2 lambda_2=0xx (-5)+2 xx (-3)=-6`

That shows third line is in line of dipendence of columns and determinant is 0