I
let X dat RA k detCA net
AEMan IR
BasisStep
met
a Can
P D det Kla
uCan
Rdata
Inductionstep
Inductionhypothesis
Ansi xen
TRUE
nti
det RA
Y A EMati
detM
detA
cent
R
mt
É Cit
E
det RA
Ai E Mmm
detfka
det Mi
m
C1
Ir
it
K ai
minor
By I N
in det Ai
def RA
detCRA
E
r
f 1 it ai
detCai
n'tdetA
X TRUE
QED
2
Given
det f a
i dett
I det a
det a
iff
n even
and m o
2 Cantor
w
autbu au bus
W C au
W
austbus
Ma W
austbus
w Canstbus
w Cavitbu
a wzuz wave t blueuz wzu
a CwuzWsu
Itbcwuzwzu
a
Wa
bus
wa antbu
w can thus
a waw wins
tb
wz u wv2
wzuzwaw wuzwzu Waviwaz
tb wave wavy Wv3 way Wav w v2
It b
a cu w
w
v
linear
cross product
2
uxo
fu uz wz
x
4,02103
6203 dzV2 in uz uz U uVa Uav
CuzV2 U V3
u u
ups us v1 via
Loxu
cross
3
Assume
E
F
u u3
a a
an
i
product alternating
is
linearlydependent
O
tan
but
Itai
w xu
8
o
guv
u is scaled v
u xu
g
u xu
FCCu usv3 x usVail
n xu
g cuzu VavaVivaVal
g
o
u uz van
0,0 3
contradicting
u
xo
0
false
supposition
if v.v is
linearlydependenuxuto
3 x
I
detcan
IMis
mi
uppert riangular
matrix in Imman Cr
Basisstep
n
mi
m
M
IT
m
in
a TRUE
Inductivestep
IM
tn s 1
X
TRUE
n
to show X nti
It
ie
det a
Mii
m
i
mm
expandinddet
m onnt
det M EY
as
ment
C it't mm det anti
ji EIR
C int tnt
defon
det me Mnt
as Mnt nt
t
0
E
m i
det M mutant
mat my det
Mnt
det
Muy n
QED
mt
mina
R
II Mii
det M
Em
IH
IT
mii
Manti nti
4
let 7 p p3
817
is
I
1 11
c
L
Tcu
i
2
Suppose
MatrixM
a
7
u
r o
so
tree
is Tranfont inv
Mmo
Moo
over
detM det M m
at M detm
det
as air 0
ever
M
deter
Mao
det m
detCon 0
so
nel
T notinutinewertible asdet m o
S
Given
I l
a b c
a y g
Mf
1
detox
la
I I
If
det
p p
expanding
ba
f
t o o
a ba ca
p p
insoul
ca
fp.az ezas
Ea
detent
ba
out
factoring
fa
ba
btacta
Ga
I
b a c a ate b a
b a c a Cob
t at btc
det M O
N
M is non invertible
from i
p