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Lecture 14

MTH 208 Lecture Notes - Lecture 14: Mexican Peso, Graph Theory, Path Graph


Department
Mathematics
Course Code
MTH 208
Professor
Herman
Lecture
14

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re
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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