Find the basis for the column space, the rank, and the nullity of a matrix.
Enter matrix entries as valid numbers. Invalid entries are rejected.
Rank
3
Nullity
0
Basis vectors
The column space is the span of a matrix's columns. Its dimension equals the matrix rank, and the pivot columns of the original matrix give a basis.
Pick the number of rows and columns you want to analyze.
Invalid cells are rejected rather than becoming zero.
The result panel shows the rank, nullity, pivot columns, and basis vectors.
Matrix with columns [1, 2, 3], [2, 4, 6], [3, 6, 9]
The column space is one-dimensional, so a basis is [1, 2, 3].
No. It always contains the zero vector.
Reduce the matrix to row echelon form, then take the original pivot columns.
Nullity is the number of free variables, equal to columns minus rank.
They identify the independent columns that span the column space.
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