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# System prepended metadata

title: LA Ch.4
tags: [LA]

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---
tags: LA
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# 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.
$A = [\matrix{1 & 1\\ 1 & 2}] \rightarrow
R = [\matrix{1 & 1 \\ 0 & 0}] \\
Row A = Row R = Span\{[\matrix{1\\1}]\} \\
Col A = Span\{[\matrix{1 \\ 2}]\} \neq span\{[\matrix{1 \\ 0}]\} = Col R$