Matrix Rank Calculator

Your details

How many rows your matrix has.
How many columns your matrix has.
Enter all matrix entries as numbers separated by commas, going left to right, top row first. For a 3x3 matrix you need 9 values.
RankRank-deficient
2

Number of linearly independent rows (and columns)

Nullity1
Maximum possible rank3
Row space dimension2
Column space dimension2
Full rank?No
Pivot positionsrow 1 col 1, row 2 col 2
2
Zero matrix<0.5Low rank0.5-2Partial rank2-3Full rank3+

Rank 2 of 3: this matrix is rank-deficient.

  • The matrix is rank-deficient: rank 2 is less than the maximum possible rank of 3.
  • This means 1 row(s) are linearly dependent on the others and contribute no new information.
  • The nullity is 1, so the homogeneous system Ax = 0 has 1 free variable(s) and infinitely many solutions.
  • By the rank-nullity theorem: rank (2) + nullity (1) = number of columns (3).

Next stepA rank-deficient matrix is not invertible. If this is a coefficient matrix, the system Ax = b may be inconsistent or have infinitely many solutions.

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