How to Find Column Space

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

1. Convert the matrix to Reduced Row Echelon Form (RREF)
2. Identify the pivot columns in the RREF
3. 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:

• Column space = span{column 1, column 3}
• Dimension = number of pivot columns