Column Space Calculator - Multi-Tools

Column Space Calculator

Find the column space (range) of a matrix with step-by-step solutions.

The column space of a matrix A is the span of its column vectors. To find it:

Convert the matrix to Reduced Row Echelon Form (RREF)
Identify the pivot columns in the RREF
The corresponding columns from the original matrix form a basis for the column space

For example, if matrix A has RREF with pivots in columns 1 and 3, then:

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