EC40 2 49th MT WK7 REVISED Proof Of - London School of ...personal.lse.ac.uk › sabharw5 ›...
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EC40 2 49th )
MT WK7 -
REVISED Proof OfVASSILIS PS4 Q 347¥ )
RAGVIR's SPEAKING NOTES
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HERE IS A copy - PASTE OF MY"
04 -mtwk 5 part 3. Pdf
"SLIDE ,
LQ3 ) . RV ZE1R"
,e ~ µz, Vz) I
• Constantq
C- R"
.
Define w : = q'
Z.
Find Elw ) and Vario ) .
F- 4) = of ELZ ) = q'µz .
Vary ) = of Varq
= of Vzq .
lifeIii)
✓
4) since there exists a qto sit.
Var E) = 0,
there is a perfect linear relationship betweenelements of z
.
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HERE IS MY REVISED PROOF FOR ABOVE ;
. Let's assume
IWLOG) that there exists just ONE vector of to sit
. Varley'2) = 0.
• Then, recognise the following results :
i. Var 4 = of Vzq = 0 iff Vzq = 0 for qf0 ;
2. Null :-.{ off IRN / Vzq = 0 } and twos
Nullity dim { Null the ) } = I;
3. By the rank - nullity theorem,
rank (4) +
Nullity(E) = N
.
• By 1,2 ,
and 3,
rank µz) = N - I.