Lecture2- Sep 29 A singular system :

Matrix times vector 2u+ vt w= 5r

By rows : 4ut2v+ 2W = n

Gu - Go = -2

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)=k÷¥¥¥⇒i

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#Elimination :

By columns : 2ut vt w=5

a Hts .Huey :# - mornin.wlo±I÷In general :

Other possibilities :ask.ae#meiaa:Ixt*dA.!Xx

(d)

m rows , n±columns n= entries -

Another singular system :

ax *

ftp.M.t.txnfaaanynnfi?gHauuIrtzFts

µ sat rtawgfHfNo solutionA line

h entry : ainxitaizxzt . . tainxn of soln's

= nfaaijxj .

( b '(e)

EliminationColumn picture ut vt w=2

-

2ut 3W=5

ukf.io/Y+wfff=bsat

r+aw=7/ Rz → 122-2121

R3→ 133-3121

at vt w= 2→ 3 columns in a plane .

- Lot w=1- 2vt W=l

[ col 2 = 3611 ) - Had 1)] f Rs → Rs - Rz

Can solve only If b is in

Lutvt w=2

that plane . II. =L

- 0=0

system in Echelon Form•b - -

i

heading variables : uiv

ad2•

b Free variables : wa.%¥.tn#IatiEanaksFtaiETni:Ia

¥1✓ ' at ' ' w⇒v=÷+ ,

x manyU=£f{ + E) - w=£ - zw

solutions.

For each SER , get a sdn atw=S :

Pahindeadrodmwmmbiawainonsof two Kf =f¥¥if

vectors stay in the plane ofthe two vectors

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