The rank of a matrix is the maximum number of linearly independent row vectors (or column vectors) in the matrix.

The rank is found by reducing the matrix to its row echelon form and counting the number of non-zero rows.

Allowed Row Operations:

• Swapping two rows: \( R_i \leftrightarrow R_j \)
• Multiplying a row by a non-zero scalar: \( R_i \to cR_i \)
• Adding a multiple of one row to another row: \( R_i \to R_i + cR_j \)

This calculator demonstrates this process step-by-step.