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.