MA 35100 Lecture Notes - Lecture 9: Cross Product, Solution Set, Linear System
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" goal of 1. 4 : fix matrix a. Understand how the solution set of the linear system w/ avg . matrix [ aib] changes as b changes . Linear system : a , , , "/ + _ . am z am i. " column space : the span of the columns of a matrix a. " written cot (a) or cot space (a) Theorem 1. 8 : a linear system with coefficient matrix a and vector of constants b is consistent iff be col space (a) . For those b for which the linear system with avg. matrix [ al b] is consistent , how do the solution sets compare as we vary ? columns. An ] c- m ( msn ) and c- 112h , then we write ax as shorthand for. , a , + z az . N an and call it the matrix - vector product of a and x .
