Column Space Calculator

The column space (also called the image) of a matrix A is the set of all possible linear combinations of its column vectors. A basis for the column space is a set of linearly independent vectors that span the space.

The Process:

• Step 1: Reduce the Matrix. Transform the matrix into its Row Echelon Form using elementary row operations.
• Step 2: Identify Pivot Columns. A pivot is the first non-zero entry in each non-zero row of the echelon form. The columns containing these pivots are the "pivot columns".
• Step 3: Find the Basis. The basis for the column space is the set of columns from the original matrix that correspond to the pivot columns you identified in the row echelon form.