Math Calculators

Matrix Rank Calculator (2×2)

Determine the rank of a 2×2 matrix — the number of linearly independent rows.

Determinant —

Rank —

About the Matrix Rank Calculator (2×2)

The rank of a matrix counts the number of linearly independent rows (or columns) it has. For a 2×2 matrix, the rank can only be 0, 1 or 2.

Formula: Rank = 2 if determinant ≠ 0 · Rank = 1 if determinant = 0 but not every entry is zero · Rank = 0 only for the all-zero matrix

Rank determines whether a system of linear equations has a unique solution, and is essential in understanding matrix invertibility.