MTH 114 Lecture Notes - Lecture 25: Mexican Peso, Null Character, Row And Column Spaces
Document Summary
It"s of an mxn matrix a, writen as nul a, is the set of all solutions of the homogeneous equation ax=0. Nul a = {x : x is in r^n and ax=0} The term space in null space is appropriate bc the null space of a matrix is a vector space. There is no obvious relation b/w vectors in nul a and the entries in a. Nul a is defined implicitly, bc it"s defined by a condition that must be checked. No explicit list or description of the elements in nul a is given. However, solving the equation ax=0 amounts to producing an explicit description of nul a. It"s of an mxn matrix a, written as col a, is the set of all linear combinations of the columns of a. Col a ={b : b = ax for some x in r^n}
