If some column of m:1trix A is a pivot column. then the

M303 Section 4.2 Notes- Null Spaces, Column Spaces, and Linear Maps 10-28-16  Matrices and linear maps give many examples of subspaces  Null space of × matrix - denoted ; set of solutions to homogeneous equation = , notated = ℝ : = } o Set of all ℝ mapped into zero vector of ℝ via linear transformation = o Finding means solving = ; parametric vector form of solution gives spanning set to explicitly describe null space 1 −3 −2 o Ex. Let [ ]. Is = 5,3,2 in