The Null Space (Kernel) of a Matrix
Matrix Algebra DS practice problem on Onlearn.
Difficulty: medium.
Topics: Understanding the Null Space (Kernel) of a Matrix via Gaussian Elimination, Augmented Matrix, Pivot Identification, Back Substitution, Parametric Solutions, Floating Point Epsilon, Linear Algebra, Vector Spaces, Numerical Computing, Matrix Calculus, Linear Systems, Gaussian Elimination, Rank-Nullity Theorem, Basis and Dimension, Row Canonical Form, Free vs Pivot Variables.
Given a matrix A (represented as a list of lists), compute a basis for the null space (kernel) of the matrix. The null space consists of all vectors x such that Ax = 0. Return the basis vectors as a list of lists. If the null space only contains the zero vector, return an empty list.