Column Space Calculator

Your details

Number of rows in the matrix.
Number of columns in the matrix.
Rank (dimension)
3

The number of linearly independent columns - dimension of Col A.

Nullity0
Basis vectors[1, 0, 2], [2, 1, 5], [1, 3, 0]
Col A spansCol A = R3 (full column rank - the columns span the entire space).
Rank (dim Col A)3
Nullity (dim Null A)0

Col A has rank 3 and nullity 0.

  • The column space has dimension 3, meaning 3 of the 3 columns are linearly independent.
  • Nullity = 0, so the only solution to Ax = 0 is the trivial solution. The columns are linearly independent.
  • The matrix has full row rank (3 = m = 3): the system Ax = b is consistent for EVERY b in R3.
  • The matrix is square and full rank, so it is invertible.

Next stepCol A = R3 (full column rank - the columns span the entire space).

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