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

5x + 3y + 7z = 4

3x + 26y + 2z = 9

7x + 2y + 10z = 5

Question

Show that each of the following systems of linear equations is consistent and also find their6x + 4y = 29x + 6y = 3

Philoid · Accepted Answer

The above system of equations can be written as

or AX = B

Where A = B = and X =

|A| = 36 – 36 = 0

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

C₁₁ = (– 1)^{1 + 1} 6 = 6

C₁₂ = (– 1)^{1 + 2} 9 = – 9

C₂₁ = (– 1)^{2 + 1} 4 = – 4

C₂₂ = (– 1)^{2 + 2} 6 = 6

Also, adj A =

=

(Adj A).B =

=

Thus, AX = B will be infinite solution,

Let y = k

Hence, 6x = 2 – 4k or 9x = 3 – 6k

X =

Hence, X = , Y = k

Show that each of the following systems of linear equations is consistent and also find their
6x + 4y = 2

9x + 6y = 3