For the system of equations

AX = B

Write [A:B] by adding the column of B to A.

[A:B] is called the augmented matrix for the given system of equations.

1. If the rank of augmented matrix is equal to rank of the coefficient matrix, the given system is consistent.

2a. In case of m x n matrix, if m is greater than and r(A) = r(A:B) = n, the system has a unique solution.

2b. In case of m x n matrix, if m is greater than and r(A) = r(A:B) is less than n, the system has multiple (infinite) solutions

2c. Similarly, In case of m x n matrix, if m is less than and r(A) = r(A:B) is less than m, the system has multiple (infinite) solutions

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