--- tags: LA --- # LA Ch.4 ## 4.3 A = $[\bar{u_1}, \dots, \bar{u_n}]$ Col A = $Span\{\bar{u_1}, \dots, \bar{u_n}\}$ $\rightarrow$ dim(Col A) = rank A dim(Null A) = n - rank A #### E.g. $A = [\matrix{1 & 1\\ 1 & 2}] \rightarrow R = [\matrix{1 & 1 \\ 0 & 0}] \\ Row A = Row R = Span\{[\matrix{1\\1}]\} \\ Col A = Span\{[\matrix{1 \\ 2}]\} \neq span\{[\matrix{1 \\ 0}]\} = Col R$