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Corollary

For agiven matrix Avref is unique

EI suppose rrefCA of Ig where dCE Ez Es where

te IEEye Find It

She Ez Iot yf4G in Nef

CA this is also true in A

E4fIII

Similarly in rrefCA 221

1323 224

In AEse 213 Ezto TI

EII E's

Note Since clearly EI Es EIS is linearly independent in rrefCA

this is also time for columns of A

Moreover EE E3 Ex3clearly span the column space of rrefCA

Therefore same happens in It

Det column space is the space spannedby the columnsof H

In general

colspace of Aspam columnsof A3

row

space of aspanErows of A3

rankCA of leading 1Sin rrefCA

Fact rank Adin colspaceCA

rankCA din Crowspace

CA

Det let Abe mxn

aIf rank Amwe say It has full row rank

bIf rank

CA nwe say It has full columnrank

cIf men and rankCA nwe say It has full rank

EI supposestandardform LOP has initial tableau

ftp.I 6qzQdoBtnafpoassIbfbasi3 determine which

Avis babasis

afaass 119 2IEtaimY EdIem979EE

needs to belinearlyindependent

Here since 32 Cignoring objective vow it's impossible to

pivot to bases 12,33 Moreover basis

including 183 are impossible

know also fz Is 14 215,63 not possible

15 basisremained

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