Cadi Kyi - University of California, San Diego
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Friday April 9 press record LAST CLASS Geometry meaning of determinant 2 2 A E Ca Cadi Kyi detAI Area of parallelogram spanned by column vectors I Carb c 3 3 A IIE of a.ge i column vectors at FTP detat upoakanfeiegtipee sv l r e l
Transcript of Cadi Kyi - University of California, San Diego
FridayApril9 pressrecord
LASTCLASS
Geometrymeaning of determinant
2 2 A E Ca
Cadi
Kyi
detAI Areaof parallelogramspannedby column vectors
I Carb c3 3 A IIE of a.ge icolumnvectors
at
FTP detat upoakanfeiegtipeesv l r e l
Geometry of Determinants part 2
When is detA o detA O del Aso
2 2 case O
A II I
f ER
angle from columnin vector 1 to columnvector2go.y.mnA
THEOREMA I detA o when 0 70
CBI detAso when 0 0
C delA O when 0 0 or.tt
Example
0fqdet 911 1 o Nz
det 9 lol l f Nz
3 3 case
A IIaT F
T
fTheorem
a detA o it upWITsatisfies therighthandof rule
detA o if a iv o lie
on a planethrough10,900
del Aco it aivia
DON'T satisfy the tighthandrule
THE RIGHTHAND RULE
ARIGHTHAND
ftpIEEE inf
f fIt
ifso.ciEofEEEEEE
I n f T
I I f Ig t
r tSATISFIES I FqeA
e ofthe rule
EXERCISE
Use geometry to compute
det IE
HETTIEdet 6
GEOMETRY ofDETERMINANT in summary
2 2 3 3
detAI AREA VOLUME
signof RIGHTHANDANGLE RULEdetA
CROSS PRODUCTS
A NEWWAYTOMULTIPLY VECTORS
RECALL
SCALARMULTIPLICATION
Input scalar Output vectorvector
Dot PRODUCT
Input vector Output Scalard vector
CROSS PRODUCT
Input Output3D vector 3D vector3D vector
ALGEBRAIC FORMULA
Cab c Nd e f Cbf Ce ed af ae bd
How to remember creatorsc
Cabchilde 1 Ifd e f
Cbf ce i laf od j1 Cae bd k
EXAMPLE
41,21 10,31
Iii03 I
L G i Il Dj f 3 o k
L 5 y
THE Vectors i j k
ixj kjxk ik.ci j
jxi k kxj i ixk j9 10 00,0 jxj 490,0 kxk Co0 o o
inD X
jk
ExerciseA Compute 1111,17 1012,37
B Compute 4 1,2 1 2,1 2
ArsA I j k
f E ni es osi
z o k
1 3,2
ASB I f onion
