MATH136 Lecture Notes - Lecture 17: Free Variables And Bound Variables, Minnesota State Highway 1, Row And Column Spaces

• School: University of Waterloo
• Department: Mathematics
• Course: MATH136
• Professor: Robert Sproule

Document Summary

Wednesday, february 10 lecture 17 : subspaces associated to matrices. 17. 1 definition let am n be an m by n matrix. The nullspace, null(a), of the matrix a is defined as follows: Null(a) = {x n : ax = 0}. Determining the nullspace of a matrix a essentially comes down to solving a homogeneous system of linear equations. If t : n m is a linear mapping which induces the matrix a then. We know that the solution set s of a homogeneous system of linear equation is of the form s = span{a1, a2, , am}. Null(a) = span{a1, a2, , am} is a subspace. By checking the linear independence of the spanning family {a1, a2, , am} we can determine whether this spanning family is a basis of null(a) or not. 17. 2 definition let am n = [c1 c2 cn]m n be a matrix.