L : (IB , V ,
+) >
-
(IR ,
W
, t) lineaire
affolding
↳ Sie d = Een , ..., wil basis V
van
&We , wmb basis W
B =
...,
van
matrikvorstelling L EPm : van
Legenerer uß
~ in in kolom rop(((wi)
Speciaal grat
matri van
basisverandering
Stel L' vor een basis van
V
van 6 Maar d : Id"
↳ in irkolom : (Id(Will =
zo (Mil
, 7) Beschou de lineaire Transformatie
lineaire Transformatie ~
T:
:f --
f" 48 f
-
+
Vind de makris To meta = (X, 1+X
,
x + x2, X3)
T(x) = -
4 + X
=
cor(X -
4) =
(5 -
4 0 %
1.
, , ,
T(+ =
-
4 + 1 + x =
3 + X
=>
en(x -
3) =
(4, -
3
,
0
,
0
T(x + X 2) =
Z
-
4 -
8X + X+y = X2 -
7x -
z = aX + b(1+ x) + e(x + 2)
+
+ d(X))
E &
-
z = f b = -
2
- 7 = a + N + z =
> 2 = 1
1 = 2 a = -
6
& = d d = 0
= 202(x2x - ) = ( -
6
,
-
2
,
1
,
%
↑ (3) = 6x -
12xi + X3 =
aX + b(1+ x) + e(x + 2)
+
+ d(X))
& &
18 = a a 10
=
G a + v + 2
I V = D
= -
-12 = 2
2 = - 12
1 = d d = 1
=>
20p(x3 - 12x + xx) =
(15 , 0. - 12
, 7)
T =
(f eI D
, 11) Beschouw de lineaire afbalding
L : IR[X]24 -
> 192 :
a + by + ex + dy3 + eXY -> (a + b ,
e + d + e)
en de basis d =
41, 1 + X , ( + +" ,
(n + H3 , (1 + 41")voor(R & [X] )
<4 , +
B <(1 1) (11 113 (10 , 192 /
en = -
voor +
, ,
a) Bepaal de matrix van
basisverandering van 2 naar de Standaardbasis
van (R[X] 4
↳ (1 ,
x
,
x2
,
73 , 44)
Bepaal Fd's
futt)" =
1 + 4x + 6x2 + 4x3+ +"
Tip driehoe Pascal
(e I
11 1
-
:
-naar Standaardbaris gran is gematheligte
1 Ed wa
(1 ,
Id
0
11 1 -
↓ > 1 ++ ,
0
,
0
, %)
13
Z 1
a
1
en ee
O 1 4
1337 1
,
7
,
1 ,0
, 8)
D O 1
14641 1
,
3
,
3
,
1
, 01
↑
14 , 6 , %, 1)
b) Bepaal de X X3+ X
*
Een
coördinaten van + spachte van de basis
*
erie 1 X + X" + X" = a + b(1 + x + e( + + + + d(y ++ ) + e( + +4
X x x4 2eX + ex + d + 3dX + 3dx"+ dX3
+be
+ + = a +
-
+ Extext-
X + 13 + X" = a+ b+ 1 + d +e + ( + z + 3d + be)X + (e + 3d + 6e)x
+ (d + 4e)X3 + exY
E &
a + b e+ d +
+ e = 0
1
a = -
0 -
3 + 3 - 1 = -
b+ 22 + 3d + 4e = 1
b = 1 -
4 -
3 + 6 = 0
& = >
2 + 3 d + be =
2 =
3
d + he = 1
d =
-
3
l = 1 e =1
con(X + y3 + xx) = ( - 1
,
0
,
3
,
-
3
, 1)
>
-
pliez 20s(X + X x 4) + = (0, 1, 0, 1
, 1)
200(x + + + +4) Idd 20s (X ++ 4)
3
= -
++
(F)
2) Bepaalde matritvoorstelling van Lor de Standaardbotissen en
Mor de basisten 2
ent
E = [n =
(1 1 7
/
44, 43 ,
74
d =
Ep ((1 =
, 02 , 10,273
, (m) = (1 , 0)
Ei =
4(0) , (91)
-
j
-
-
(A) =
(1 d ,
((xz) = ( 0
,
1) 1 h
-
>
(1 , 0 (1 p ,
L(x3)
((tY)
=
=
(0,
(1)
1)
iin
(0 , 1) -(0, 1
et (1) (91)
= (iii)
Li hoe B hee
=
, (ir
Teplie
((n) =
(1 , d) (1 , 0) = a(1 , 1) + b(1 , 1) -
b
(1 a
= +
0 = a -
v
Ex v =
1
(z , 0)
a
((1
=
+ y) =
4 2
z = a+
D = a
-
b
L(GHz) =
(3 , 1) Es a = b = 1
>=
E
28 + 1 3 1
b
=
[
=
3 = a +
1 = a
-
V(sa = 1 + v
(((1 ++ (3) =
(y , 4) = a =
2
b
(44
= a +
=
a
-
b
4
Es(a4
= 4+ e = a =
L((nex) =
(5, 11) = 4 + 2b = b = 0
Er
( =
(3)
-rie 2
Li = VOVT :
prober
I
L (d)
↳ michervor
(a)
=
() E =
+) >
-
(IR ,
W
, t) lineaire
affolding
↳ Sie d = Een , ..., wil basis V
van
&We , wmb basis W
B =
...,
van
matrikvorstelling L EPm : van
Legenerer uß
~ in in kolom rop(((wi)
Speciaal grat
matri van
basisverandering
Stel L' vor een basis van
V
van 6 Maar d : Id"
↳ in irkolom : (Id(Will =
zo (Mil
, 7) Beschou de lineaire Transformatie
lineaire Transformatie ~
T:
:f --
f" 48 f
-
+
Vind de makris To meta = (X, 1+X
,
x + x2, X3)
T(x) = -
4 + X
=
cor(X -
4) =
(5 -
4 0 %
1.
, , ,
T(+ =
-
4 + 1 + x =
3 + X
=>
en(x -
3) =
(4, -
3
,
0
,
0
T(x + X 2) =
Z
-
4 -
8X + X+y = X2 -
7x -
z = aX + b(1+ x) + e(x + 2)
+
+ d(X))
E &
-
z = f b = -
2
- 7 = a + N + z =
> 2 = 1
1 = 2 a = -
6
& = d d = 0
= 202(x2x - ) = ( -
6
,
-
2
,
1
,
%
↑ (3) = 6x -
12xi + X3 =
aX + b(1+ x) + e(x + 2)
+
+ d(X))
& &
18 = a a 10
=
G a + v + 2
I V = D
= -
-12 = 2
2 = - 12
1 = d d = 1
=>
20p(x3 - 12x + xx) =
(15 , 0. - 12
, 7)
T =
(f eI D
, 11) Beschouw de lineaire afbalding
L : IR[X]24 -
> 192 :
a + by + ex + dy3 + eXY -> (a + b ,
e + d + e)
en de basis d =
41, 1 + X , ( + +" ,
(n + H3 , (1 + 41")voor(R & [X] )
<4 , +
B <(1 1) (11 113 (10 , 192 /
en = -
voor +
, ,
a) Bepaal de matrix van
basisverandering van 2 naar de Standaardbasis
van (R[X] 4
↳ (1 ,
x
,
x2
,
73 , 44)
Bepaal Fd's
futt)" =
1 + 4x + 6x2 + 4x3+ +"
Tip driehoe Pascal
(e I
11 1
-
:
-naar Standaardbaris gran is gematheligte
1 Ed wa
(1 ,
Id
0
11 1 -
↓ > 1 ++ ,
0
,
0
, %)
13
Z 1
a
1
en ee
O 1 4
1337 1
,
7
,
1 ,0
, 8)
D O 1
14641 1
,
3
,
3
,
1
, 01
↑
14 , 6 , %, 1)
b) Bepaal de X X3+ X
*
Een
coördinaten van + spachte van de basis
*
erie 1 X + X" + X" = a + b(1 + x + e( + + + + d(y ++ ) + e( + +4
X x x4 2eX + ex + d + 3dX + 3dx"+ dX3
+be
+ + = a +
-
+ Extext-
X + 13 + X" = a+ b+ 1 + d +e + ( + z + 3d + be)X + (e + 3d + 6e)x
+ (d + 4e)X3 + exY
E &
a + b e+ d +
+ e = 0
1
a = -
0 -
3 + 3 - 1 = -
b+ 22 + 3d + 4e = 1
b = 1 -
4 -
3 + 6 = 0
& = >
2 + 3 d + be =
2 =
3
d + he = 1
d =
-
3
l = 1 e =1
con(X + y3 + xx) = ( - 1
,
0
,
3
,
-
3
, 1)
>
-
pliez 20s(X + X x 4) + = (0, 1, 0, 1
, 1)
200(x + + + +4) Idd 20s (X ++ 4)
3
= -
++
(F)
2) Bepaalde matritvoorstelling van Lor de Standaardbotissen en
Mor de basisten 2
ent
E = [n =
(1 1 7
/
44, 43 ,
74
d =
Ep ((1 =
, 02 , 10,273
, (m) = (1 , 0)
Ei =
4(0) , (91)
-
j
-
-
(A) =
(1 d ,
((xz) = ( 0
,
1) 1 h
-
>
(1 , 0 (1 p ,
L(x3)
((tY)
=
=
(0,
(1)
1)
iin
(0 , 1) -(0, 1
et (1) (91)
= (iii)
Li hoe B hee
=
, (ir
Teplie
((n) =
(1 , d) (1 , 0) = a(1 , 1) + b(1 , 1) -
b
(1 a
= +
0 = a -
v
Ex v =
1
(z , 0)
a
((1
=
+ y) =
4 2
z = a+
D = a
-
b
L(GHz) =
(3 , 1) Es a = b = 1
>=
E
28 + 1 3 1
b
=
[
=
3 = a +
1 = a
-
V(sa = 1 + v
(((1 ++ (3) =
(y , 4) = a =
2
b
(44
= a +
=
a
-
b
4
Es(a4
= 4+ e = a =
L((nex) =
(5, 11) = 4 + 2b = b = 0
Er
( =
(3)
-rie 2
Li = VOVT :
prober
I
L (d)
↳ michervor
(a)
=
() E =
