SLE – Rank of a Matrix and Consistency of Systems

In a matrix, the rank is always ≤ the minimum of (m, n),
where m, n indicate the dimensions of the matrix (m × n).

Types of systems

• SCD = Sistema Compatible Determinat (una solució)
  → Consistent System with a Unique Solution

• SCI = Sistema Compatible Indeterminat (infinites solucions)
  → Consistent System with Infinitely Many Solutions

• SI = Sistema Incompatible
  → Inconsistent System (no solution)

Matrix Rank in Python

<p>Three 3×3 cases to illustrate rank: identity (3), dependent rows (2) and dependent columns (1)</p>