🔷13 - Consistent and Inconsistent System of Equations

🔷13 - Consistent and Inconsistent System of Equations

In this video, we are going to discuss consistent and inconsistent system of linear equations. Given that Ax = b, is a system of m linear equations and n unknowns, where A = coefficient matrix, [A | b] = augmented matrix
if the rank of A = rank of [A | b], the system is consistent.
in a consistent system
if
the rank of A = rank of [A | b] = n (unknowns), the system has a unique solution and
if
the rank of A = rank of [A | b] is less than n (unknowns), the system has infinitely many solutions.

However if the
rank of A is not equal to the rank of [A | b], the system is said to be inconsistent and the system has no solution.

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00:00 - Consistent and Inconsistent Systems
02:23 - Example 1
11:32 - Example 2