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

Show that each one of the following systems of linear equations is inconsistent2x + 3y = 56x + 9y = 10

Philoid · Accepted Answer

The above system of equations can be written as

or AX = B

Where A = B = and X =

|A| = 18 – 18 = 0

So, A is singular,Now X will be consistence if (Adj A)xB = 0

C₁₁ = (– 1)^{1 + 1} 9 = 9

C₁₂ = (– 1)^{1 + 2} 6 = – 6

C₂₁ = (– 1)^{2 + 1} 3 = – 3

C₂₂ = (– 1)^{2 + 2} 2 = 2

Also, adj A =

=

(Adj A).B =

=

= ≠0

Hence, The given system is inconsistent.

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

6x + 9y = 10