The column space of a matrix
Matrix Algebra DS practice problem on Onlearn.
Difficulty: medium.
Topics: Understanding the Column Space of a Matrix, Pivot Columns, Row Echelon Form, Elementary Row Operations, Column Rank vs Row Rank, Orthonormal Basis, Linear Algebra, Vector Spaces, Matrix Theory, Numerical Analysis, Computational Geometry, Linear Independence, Basis of a Subspace, Rank of a Matrix, Gaussian Elimination, Span of Vectors.
Given a matrix A, find the basis for its column space. The column space is the span of the linearly independent columns of A. Return the original column vectors that form this basis.