Show that each one of the following systems of linear equations is inconsistent

x + y – 2z = 5


x – 2y + z = – 2


– 2x + y + z = 4


|A| = 1(– 3) – 1(3) – 2(– 3) = – 3 – 3 + 6


|A| = 0


Cofactors of A are:


C11 = (– 1)1 + 1 – 2 – 1 = – 3


C21 = (– 1)2 + 1 1 + 2 = – 3


C31 = (– 1)3 + 1 1 – 4 = – 3


C12 = (– 1)1 + 2 1 + 2 = – 3


C22 = (– 1)2 + 1 1 – 4 = – 3


C32 = (– 1)3 + 1 1 + 2 = – 3


C13 = (– 1)1 + 2 1 – 4 = – 3


C23 = (– 1)2 + 1 1 + 2 = – 3


C33 = (– 1)3 + 1 – 2 – 1 = – 3


adj A =


=


Adj A x B =


=


Hence, The above system is inconsistent.


4