Given as 5x + 3y + 7z = 4
3x + 26y + 2z = 9
7x + 2y + 10z = 5
The given equation can be written in matrix form
|A| = 5(260 – 4) – 3(30 – 14) + 7(6 – 182)
= 5(256) – 3(16) + 7(176)
|A| = 0
Therefore, A is singular. Thus, the given system is either inconsistent or it is consistent with infinitely many solution according to as:
(Adj A) x B≠0 or (Adj A) x B = 0
Co-factors of A are
C11 = (– 1)1 + 1 260 – 4 = 256
C21 = (– 1)2 + 1 30 – 14 = – 16
C31 = (– 1)3 + 1 6 – 182 = – 176
C12 = (– 1)1 + 2 30 – 14 = – 16
C22 = (– 1)2 + 1 50 – 49 = 1
C32 = (– 1)3 + 1 10 – 21 = 11
C13 = (– 1)1 + 2 6 – 182 = – 176
C23 = (– 1)2 + 1 10 – 21 = 11
C33 = (– 1)3 + 1 130 – 9 = 121
Now, AX = B has infinite many solution
Let z = k
Then, 5x + 3y = 4 – 7k
3x + 26y = 9 – 2k
This equation can be written as
