MATH1002 Lecture Notes - Lecture 11: Free Variables And Bound Variables, Coefficient Matrix, Linear Combination

• School: University of Sydney
• Department: Mathematics
• Course: MATH1002
• Professor: Nathan Brownlowe

Document Summary

What does it look like and what are its properties. Rank:the number of non-zero rows in row-echelon form. Can be used to determine the number of free variables in a system. If the number of variables is greater than the rank of a system, we will have a free variable. For any matrix a, dim(row(a)) = dim(col(a)) Rank theorem: let a be m x n matrix. Then, rank(a) = dim(row(a)) rank(a) = rank(at) rank(a) + nullity(a) = n (the number of columns) Rank and null space of a are not changed by row operations. The cardinality of a basis for null(a) = # of free variables. The span of a set of vectors in rncan have any number of. S = {v1, , vm} dimensions from 0 to n. If there is a vector b in the span of some vector set s, there is alwayssome other set. = [ 1, 2, 3, , m] such that s = b.