MA 35100 Lecture Notes - Lecture 20: Solution Set, If And Only If, Mexican Peso
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#elements in basis of cal (a) in solution to ax= b dim. of co1 (a) A ax = b dim of row (a) dim of row (at) 1 n = rank (a) basis for nullspace (a) aim nullspace (a) If ax: b has a solution, then it has a unique solution when. Recall: if ax: b has a solution, then its solution set is a translate of nullspace (a), so ax: b has a unique solution ifhullspace (a): sc ift nullity: Theorem 2. 18 rank (a) = n. soh iff. If i is man, then ax: b has at most one solution for every b-r4 itrank (a) = 1. Recall: if a is man, then ax: b has a solution for every berk iff. " a is non - singular if ax = b has a unique solution for every b.
