MATH 1ZC3 Lecture Notes - Lecture 1: Mexican Peso, Coefficient Matrix, Ibm System P

• School: McMaster University
• Department: Mathematics
• Course: MATH 1ZC3
• Professor: Francesc Font

Document Summary

Rank = # leading 1"s in re (& thus in rre) of the matrix e. g. 2. Soln: put leading 1 in upper left corner. , note leading ones in 1st and 2nd column. Coefficient = a; x = variable, b = constant n = r+p. , where a = n and b = 1. R = rank = leading 1"s =#var"s w. own eqn in simplified system. P = #free variables= #parameters - relates to uniqueness. Contradictions: no solutions arise [0 0 0 0|# 0] Note, the first two columns are a, 3rd is b, and all are avg. , in general, if avg has rank>rank a, inconsistent. Let a = coefficient matrix, a b avg matrix of a linear system. If n > rank(a) --> p>0, infinite solutions ( rank a b . If it is inconsistent, n = r+p n , can"t have more leading 1"s than columns.