Show that each of the following systems of linear equations is consistent and also find their
Solution:

x + y + z = 6

x + 2y + 3z = 14

x + 4y + 7z = 30

Question

Show that each of the following systems of linear equations is consistent and also find their2x + 3y = 56x + 9y = 15

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 =

=

Thus, AX = B will be infinite solution,

Let y = k

Hence,

2x = 5 – 3k or X =

x = 15 – 9k or X =

Hence, X = , Y = k

Show that each of the following systems of linear equations is consistent and also find their
2x + 3y = 5

6x + 9y = 15