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Different
D.
Mini case
Geometry
⇐
:
& Algebra Gedney
manning
-
Herd
pylon
simple seeming
-
a
tut the
It turns at
A hdv
qagtn Hu
Thi
f
:
sort
pytn
TirstS=h
lines
so
1123
,
in
to
ag
Project hize
with
the piste I dmsin
now
uhd
may
the
are
para
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uht das
a
f
&
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hyppke
in
lyj
lines
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y,
the
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,
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instead
c-
Rn
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so
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oeydf
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miwf
into doth
ale
specify
a
1
me
easy
to
an
f
lie
tfh
the
the
(
if they intmut , ek
see
Grass
a
by
to the debt point
oBm
ling
gun
hd to find at last
so
p.tl
ERP
pntte
comedy the
,
z
1133
in
R?
in
RIP
ask
not
one
all 3
toss through
birth algebra gamely
can
1k
&
,
munis
.
the op
.
n
RD
but
,
.
.
he
see
Hit
{ lxih ZAKIR
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lines
whihfom
,
P
in
a
4
lie pnb
.
gy
f
in
RIP 3) anespd to
Mph aspty
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of
lines
at
ktnitj :
down :
& ask Hw myths in
the in
.
the met
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rephrase
.
meme this
(h A)
1ms
.
lines
may
,
that 4 gun
my genesis
.
So
mtmikty
lines
at the
ponb in R ? The except
So
1133hew
spoiled by dta
belter approach B to
Now by identifying
,
Gian 3 lines in
together with
)
gin to
are
may
Its not
:
( i.e. ,
A
lies
:
RIP
3
RIP ntxet
,
4
t { lxn HBU { lines at D)
,
neat , nfnily
gun
1ms ?
look like
in
"
"
The
advantage B
th } Piche ?
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tt la the
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spare
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anew
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s
apt
iplr
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lie
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in
.
z
,,
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army
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plane in IR ?
&
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vie
versa
a
,
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phone in IR
ddu
either
is
1rem
a
{lx HD
,
or
%
RP at
"
the
in
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D}
determines
Ptnn Ru
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,
infinity
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-
,
Of
the
case
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hit just
the lines
Seandsiyyh
define
fnd
pwhiy
Nn,
Equivalently , think
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Also
,
if
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ylp)
you
( fns
B
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if
is
ctgy
at
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GDR
in
so
,
tht
see
we
621124
g.us
the
all lion IRIP
f
Spare
.
with
identity 621124
shot
a
ref
IRPNfor
of
is
a
I
I &
N,
same
:
xi
'
bsis
ffr
of
a
in
Phickr
mk 2
wet to
we
many
f
Yi
's
I
( Yn
FD
the rk 2 hhx
rehht G
are
,
,
'
xzy, :X , ys
-
nbptt,
the
que
a
b)
& Y =Go " hi xi
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'
for p th
ad be
:X
,
yy
:
xuy ,
-
f
:
XZY 5×342
nhnxhsrk 2 & here at test
me
gaps
pw
XZYU
ftse
,
to she
and
,
then
6,1124
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.
× 442
:
X 344 ×4 YD
-
cards moot be
Rp ?
in
xD
}y ,
x
-
if PE
Specifically ,
.
RIPGY
=
aekf
point
a
make
i.e. the mhies
.
.
) ( × yz
ditht
by a
.
2×4 retries
f
) } fr P &
Sae span
(P
→
lxo : a
g-
f
with quid me Asses
he th
ms
these Pont
f
)
xnxsx 91,5=4 " Yu 's, 44
sine
prlidrapkf
the determinant
"
4 : 621124
this
so
origin
man
RPN
→
their
if
fall, tht
,
the
}
in 621124
{ a tx
the mp
nonzero
brass
.
guilt
fat
,
621134
↳
a
are
we define
Note
,
,
went to
we
uidnttgpnb
so,
we an
Now
:
1124
Bh the
pay
:
4
mp
a
po do
f
spare
in
planes
-
.
RIP
case
Since
the
&
embedding
the kxk minors of the
of
.
the
I
ii
,
as
=
dye
this
get
todoktpnb
as
.
mp
the
kxnmtixgivy
thx
T
=
citdy
of bsismhx lab
-
s
k)
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hat dying
&
mean
bus
as
msyh
he in RIP
3)
if ahhtetht
ad be to
-
,
,
so
-
.
Dan
a
&
RIP utih detonate
in
ab eddy
fr
GM
"
the k plane
.
→
)
,
RPK
)
-
I
gin
by
record
of
all
Of
case
,
"
GDR
Tf
not all
points
4-dims il
,
write 41N
we
↳)
Pnp
Chtk : For P
,
Pi 3 Pz 4 +
}y
:
3
,
:
Pin
Pa : Put
Ply R3
), HP) ( × yz
=
,
the
in
are
41124 mob th }
imgef
shldeypat 416,1124 ) to be
we
I Piz :P
=
-
LI }
=
RIP
in
5
) , the
By
the
by
qnhh
a
side girth
is S
-
if &
dims
.
13
=0
.
xzy, :X , ys
-
,
:
determined
Since RIP
mp
.
X }Y ,
-
:X
Yy
,
-
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!
In
th }
may
system
f)
particle,
1
a
↳
So now
'
.
the stock
Kinsel
6,1124
we
begin 4
Rp5 satisfy qndim G)
's
points
Df
For
'
.
a
in RP sadly
nested
sqme
Gg :
Tfl
Png ht
:
,
}
01
,
a
a
fie
<
.
Ai
then the
=
a
,
.
the delimit
Ao
,
sit
,
-
having
< an
.
:
st
.
Ao,
Pjo ju
.
.
.
.
.
,
±
xa ;
:
=
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,
.
;
0
n
-
all
Cnd
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1mg
:O :
.
.
:o) }
-
f
S A←,
in L )
determined
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liver
> ai
RIP ddqmnd
by the
uaphy if
he Y
&
6.1129
points m
4 puts in
swbgpaes
dsnbspvsf Rp
"
obey
ion
,
hi l
in
ht Ai be the
ginks
4
or
quid ntf that f
,
,
reklthskpwl the 4 gin point in RP ?
zi far all i
if
f
RM say tht Ht )
a
ai
dinsilswbspae L
obeys
,
.
the
Sohktodiln Ho
RIP intseetyl
-
-
,
.
,
An )
.
.
din 't subspm in Clp
"
'
f
pub
to the form
.
AND wdr the Ptichrhkddg 4
whnw ji
44
idnlitg
RIB ntmdj the
in
yet to be
sane
dines
& for
shut f
"
,
,
I
ig
we
RU RBDB the settling
,
.
-
,
a
.
if dim ( A
Ann
HH
to
then
RIP
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izef
by
be the
in
<
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,
And
,
.
,
Pitdmvaietg
men
h l } ke in RIP? uhih
Ao f A S Az f.
the Sdnbstadilm gin
htrtto
is
rwht to
&
he )
if
h
lines
We
.
)
a
polynomial 6)
homogeneous
:
"
GUIR
for
same
i
.
:
6km
→
NPK
"
RPM the
'
osdbf
eaog the pnbin
In
then
tai
:#
B)
:X
FYOYY
lxoh
sex
%
xi
zij
the arsenic intestd in
,
if l Erl
Ao A ,
,
the
in
conversely
the
,
)
q,
,
papsith
the
Aaf
Bt
let AOFA f
:
A
,
fun fan
.
[
=
'
,
e
Zkl
4
.
.
,
.
As { (
so
independent so
=
,
D=
''
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xo
,
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lxo :
0
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ntkthzn
eikryeyyae
ad
:o) }
& A,
:b &
q
or
=
B
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=
Ho : 4
0
:
)
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ixz
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.
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=o&K
the xi
f
are
× ' 42 : × '
:
the east
Zze
Zk
the
so
liner
,
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Zk 3
Ah
.
,
&
,
to uhih
Zee
se
Zse
2
ad ↳)
adik in the pgnsik
the
Zk
,
for
on ' '
correspond
yi to
y
%, Y"
Yi ,
.
which
deaf saws the odith
f A span
ms
if
the
the
maximizes
fm
.
zjeg
as
of the
sum
:
indices
:
:O)
zza
.
A,
,
)
dhntf slao
an
,
A,
)
.
the mtsedmf the hyprpbe {
as
on
=D in R
"
with the
.
Bo 4 B
,
f.
)
tmsfmth
)
→
) to the image f st
tht the special rfao AD
GM
RIP
IRK
Rk
f Buy
.
.
Bo
signs
hhih the the
.
,
to
be
,
Buy )
hw stops
of
f
"
Ptniwekddgf
"
tut din Aida Bit
so
itself & mps the
to
.
5
AWRY
11364
IRDEIRIP
a
Sine
saw
we
the
led :
For
,
sll
any
,
Rp 3) wheel
new
,
or
4 high h l } la
the 4
By
just the intaekfhyppts
RIP
in
,
Bake
,
the ingendr
the Ptichrabeddy is the
inter
sedmfahyprpke in Rk
?
with
So
were
hp lies :
proposition
the arrdky
,
gin
,
lines
the
BER
4)
was realized RLAO
:
5- Aa
nwtke
rl A
inge of
oo
RIP shyly B)
points in
,
linearly
zero
RIP stky
wire in kenos
new
,
=3 ,
.
zu
=
a
614=4 (
so
mlvix
Define the
he
not bth
are
ht all
me
Aine be
; E
,
in
point
ay
,
sine
) htq
Xo & xi
l =L go
So then
Pqf
not , k=2 , art
,
B
in
4 sets Uh
IRP detonate
,
silly
Ptichr
Ill
imff
,
,
IRPD
oh
n
syli
.
,
.
.
n
RPD
silly
B
,
,
RPD
IRP 3)
SB Ain
,
.
.
,
RU 4 RIPD,
,
&
the set
fksmtrady
.
4162 MY
the
Hi is
a
hyphen
IR?
i.
The ntsedm of
This play
4
"
IR
in
spared
is
2 Aims il
in lR6 B
hyper planes
2 Mets T ( h
by
=
)
The mtradmf the plane with 416.1124
(
this
a
vntbw 2) ( a
is
a
The
first
(
one
case
B
an
aztx
fling
) lny
re se
-
lab )
a
are
little bit
artifact
of
(5)
in
¢P3
,
& tht
,
,
In
ah
hg )
at the
reefs
+
(a
v
,
=
( www.s
stty
A,
,
49
w
,
,
}
.
)
w]y
way,
.
hang
ytbw g) ( a vz } tbwr 3)
0
=
,
whih either by
Et
-
Sown
a
& 6
line in RIP?
a
x2
:
-
Et
-
0
=
6=0
:
y 2=0
,
,
,
sins
solos
soks
one
one
one
1h
ty
the hwy
the line
x
x=o
&
x=y
&
o
=
Y
=
*
y
x=
o
.
.
.
land thteaetg 2
've
we
so
wwhg
.
,
Nba
in
vzy,
Xy
HI
algebra geometry
k
,
line as
"
ky ,
,
sing
solutions
as
]
plane
a
( avbtbw } ) ( a vzytbwzy )
-
solutions
as
the gown
by to be
this
tbw g)
,
double cowed
) AN
B
y
"
Iii ) 1
ii
,
form in the near
qwdrtc
l i ) 2 ( trans
li
v
,
B
,
.
i.e.
.
.
.
as
may
or
any
you
Mtmet
gwdrktns af Lethe syq
Rioted f
or
lines
,
a
more
E.
.
and
covet
restrict to RIP
3
you
an
exaple to
a
genie
point 6,0)
of
qwtupk of Ks in NP ?
as
alts
real algebra
sktht wild be tht exatf 2
serialfoot
0
or
2 Solms
)
,
-
e.g.,
geady
lines
B
iutbat
×2ti=
o
-
bit
sound hook than
a
gennzqwdsde
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