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

6x + 9y = 10

Question

Show that each one of the following systems of linear equations is inconsistent2x + 5y = 76x + 15y = 13

Philoid · Accepted Answer

The above system of equations can be written as

or AX = B

Where A = B = and X =

|A| = 30 – 30 = 0

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

C₁₁ = (– 1)^{1 + 1} 15 = 15

C₁₂ = (– 1)^{1 + 2} 6 = – 6

C₂₁ = (– 1)^{2 + 1} 5 = – 5

C₂₂ = (– 1)^{2 + 2} 2 = 2

Also, adj A =

=

(Adj A).B =

=

= ≠

Hence, The given system is inconsistent.

Show that each one of the following systems of linear equations is inconsistent
2x + 5y = 7

6x + 15y = 13