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Samenvatting Getal & Ruimte 11e ed leerboek vwo D deel 3 Hoofdstuk 11
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Samenvatting Getal & Ruimte 11e ed leerboek vwo D deel 3 Hoofdstuk 11
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Eigenwaarden d als (G) een d- (G)eigenvector is , dan is ook een
eigenvector
:
☒i. Ü = d. E
Eigenvectoren :
lineaire afbeeldingen van À naar ITÎ •
|
À het Oxy vlak
= - 1 . eenheidswetoren È ✗
= (b) en ÈG ( F )
=
kan
je vinden :
lineaire afbeelding regels : je gebruikt : als M . (b) (G )
=
en M . (9) (bd )
=
>
•
µ -0 . •
µ ( .
>
+ in> = m
>
+m dan is m= (g )
M ( di ) ✗ IMÜ)
willekeurige punten / vectoren z n
•
. =
2 . 2 bekend :
stel M = (Ibd ) en bereken a, b, c ,
d
lineaire afbeeldingen À
>
IR rotaties
van naar ,
vermenigvuldigingen spiegelingen ,
en
projecties
lineaire afbeeldingen van 1123 naar IRZ gebruik de matri:* om te berekenen waar in het
andere punt
OXY
-
vlak : n van het
gegeven
assenstelsel moeten worden
getekend
Matrix M :
spiegeling × as (I ? -
= ) spiegeling y (id ) =
spiegeling y as to ?
) -
=
loodrechte projectie g-
V2
f.ik *
=
±"
:a )
)
"""
"" " ")
spiegeling oorsprong tot -9 )
( since)
-
=
rotatie q graden =
cos ( 41
om
oorsprong over
E- M F
"
'
-
berekenen van
eigenwaarden en
eigenvectoren
M =/IÏ Karakteristieke (M d-I)
vergel king : 0
- =
(2%1.15)=1115 )
( d) ( ) -115 ) =L )
a b
•
'
(a- d
c d-
b
d) •
( ) =
(Ö ) -
oneindig veel oplö Ingen "
,
dus IMFO
( ) (II)
a b
-
( d
(% ) ik ? ) -
M -
d. I
ij ijij
ij ijij
IJ ij
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