EC40 2 49th )

MT WK7 -

REVISED Proof OfVASSILIS PS4 Q 347¥ )

RAGVIR's SPEAKING NOTES

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

.

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.