MA 35100 Lecture Notes - Thomas Say, If And Only If
Document Summary
Seo 6: theorem 1. 11 ( translation theorem) : let f be any particular solution to ax = b. Then every solution to ax = b can be written : = i + z where 2- c- null space ca) (i. e. a 2- = 0 ) . " if i lies in null space (a) Works for any solution f to ax = b not justthe translation vector . ( at = 0) , we get null space (a) again . Say = t + t , , Then = i + t , , solution i. + tic k is also a gem . solution for any particular: but also = f + sy , Ye } = nun space ca) ( = span { , E}) e : if the gen . solution from ge to ax = 0 is : s [ & ] + c- [ i ] setting e. g. s = i.
