Column Space Calculator (2×2)
The Column Space Calculator finds the rank and a basis for the column space of a 2×2 matrix. Enter the four matrix entries.
Formula
Column space = span of the matrix columns; its dimension is the rank
- If the determinant is non-zero, the columns are independent and span all of ℝ².
- If the determinant is zero, the columns are dependent and the rank drops.
[[1,2],[2,4]]
Inputs
- a₁₁: 1
- a₁₂: 2
- a₂₁: 2
- a₂₂: 4
Columns are proportional (det 0), so rank 1 with basis span{(1, 2)}.
Frequently asked questions
What is the column space?
The set of all linear combinations of a matrix's columns. Its dimension equals the rank.