Show that each one of the following systems of linear equations is inconsistent 3x – y – 2z = 2 2y – z = – 1 3x – 5y = 3

Question

Philoid · Accepted Answer

|A| = 3(– 5) + 1(3) – 2(– 6)

|A| = 0

Cofactors of A are:

C₁₁ = (– 1)^{1 + 1} 0 – 5 = – 5

C₂₁ = (– 1)^{2 + 1} 0 – 10 = 10

C₃₁ = (– 1)^{3 + 1} 1 + 4 = 5

C₁₂ = (– 1)^{1 + 2} 0 + 3 = – 3

C₂₂ = (– 1)^{2 + 1} 0 + 6 = 6

C₃₂ = (– 1)^{3 + 1} – 3 – 0 = 3

C₁₃ = (– 1)^{1 + 2} 0 – 6 = – 6

C₂₃ = (– 1)^{2 + 1} – 15 + 3 = 12

C₃₃ = (– 1)^{3 + 1} 6 – 0 = 6

adj A =

=

Adj A x B =

=

Hence, The above system is inconsistent.