Solution of a Non-Homogeneous System of Linear Equations

Three methods are there

1. Matrix method
X is obtained by finding out A^-1B

2. Determinant method – Cramer’s rule

3. Rank Method

If |A| ≠0, then the system is consistent and has a unique solution A^-1B.
If |A| = 0, and (adj A)B = 0, then the system is consistent and has infinitely many solutions.

If |A| = 0, and (adj A)B ≠ 0, then the system is inconsistent and has no solution.