Show that each one of the following systems of linear equations is inconsistent 4x – 5y – 2z = 2 5x – 4y + 2z = – 2 2x + 2y + 8z = – 1

Question

Philoid · Accepted Answer

|A| = 4(– 36) + 5(36) – 2(18)

|A| = 0

Cofactors of A are:

C₁₁ = (– 1)^{1 + 1} – 32 – 4 = – 36

C₂₁ = (– 1)^{2 + 1} – 40 + 4 = – 36

C₃₁ = (– 1)^{3 + 1} – 10 – 8 = – 18

C₁₂ = (– 1)^{1 + 2} 40 – 4 = – 36

C₂₂ = (– 1)^{2 + 1} 32 + 4 = 36

C₃₂ = (– 1)^{3 + 1} 8 + 10 = – 18

C₁₃ = (– 1)^{1 + 2} 10 + 8 = 18

C₂₃ = (– 1)^{2 + 1} 8 + 10 = – 18

C₃₃ = (– 1)^{3 + 1} – 16 + 25 = 9

adj A =

=

Adj A x B =

=

Hence, The above system is inconsistent.