Question

Show that the equations x – 3y + 4z = 3; 2x – 5y + 7z = 6; 3x – 8y + 11z = 1 are inconsistent.

Answer 1

x – 3y + 4z = 3; 2x – 5y + 7z = 6; 3x – 8y + 11z = 1 

The last equivalent matrix is in the echelon form. [A, B] has 3 non-zero rows and [A] has 2 non-zero rows. 

ρ([A, B]) = 3; ρ(A) = 2 

ρ(A) ≠ ρ([A, B]) 

The system is inconsistent and has no solution.