Math 218: Matrices and Vectors

Welcome! You have found the homepage of the Fall 2024 manifestation of Math 218.

Column Spaces

To check if v is in the column space of a matrix A, we can calculate A.augment(v, subdivide=True).rref() and look for a pivot in the augmented column.

More efficiently, we can use the Rouché–Capelli Theorem and directly check A.rank() == A.augment(v).rank().