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Samenvatting Lineaire Algebra Lesnotities | KU Leuven | 2025/2026

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Lesnotities voor het vak Lineaire Algebra aan KU Leuven, 2025/2026. De notities behandelen kernonderwerpen zoals stelsels lineaire vergelijkingen, elementaire rijoperaties, echelvorm, matrices, matrixoperaties, en lineaire afbeeldingen met basisverandering. Deze aantekeningen zijn ideaal voor examenvoorbereiding en bieden heldere uitwerkingen van voorbeelden uit de lessen.

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1
LES



(x y)
4 gradsgt
ER 3x 5
+
2y
=
,
-
Falsel
by 8
1/
=
2x -




010 opt 11 X 1


(k 193 vakken

S
14 3
y m) =
2x 74
yy
+ - =

, ,


21
Si = 1302
-




Gx) + m = 1789
0
,
1
s opl
of



& > (11 , x z , ks, .




..,
kn)




stelse van



S
ax1
11 + az +
I
...




zoff
Az171 + &zekz +...+ + Azmxm =
Ne
mug)'
enbetenden
. . .




n
met
:
Am ( +
Am2x -
+ --
+...
*
&
mmkn = Ne
(k - ,
.

.., m) ER-

(44)


lar-- ---
an (A
I
amn




Probleemstelling : Onderack of dit Stelsel gelastaan is
indien ja gof alle ge (man de gevern bepalen

, (93)

*
Tof stelsel :




/
diehacktom 302




Algemene Strategie
C F Yauss
. .
-




driehoeksvorm "Sorwer" den
Rij-operaties (ERA
elementaire rij-operaties
Pr
A X B


E
=
RitRi (X +&
P
H
.




(2) Ric &j
Ru

(3) Pi >
-

Pi +
19j


of
A




E
2y + 4n

2611 (
too
cl + =
6 24 6 R2 -
Rz -




3Pr

3x m
by 14m 16
+ + = us -




S
&z > z 23
by 114
-



2x +
-
+
= 12




Naar : echelen vorm

Term die niet nul is = leidende Kerm
leidende Tern in elke
rij
=>


:

-

links van /onder leidende Fermen : O




ry-geredvoerd + ahra : baren leidende Fermen : O




In&
! (
-ny
= 2

=
xy 3




(2)een
+n 1 = -
= -




---
22 + 2y + hm = 0 = > x = 6+ 6 -
8 = 4

offesion : <(4 ,
-3
, 2)

,(1974 %




·
x+
y+n + t =
1



t= 2
x
y
+
-

+m



3x + y + 3n 34 4
+ =




(-
A

1

1




zy
=
y E
-
1 =
-


=




variabelen nietbij leidende 1 :
vrije variabelen
variabeen bij leidende 1 :

geborder variabelen
Kies e ent
vrij (R)

Y E
= -




-
a) G =




zijkdigraden/ op I
-




homogen stelse
↳
Ziet
hier

, LES 2
parameterR
↳


E
I

I~
x +
ay
+ m = a




a 1
y
x + + an = ~ 7




ak m 1
y
+ + =




&
vrije varabelen y, n

!
:
2




glanden :




#
(f -


a)(1x a)




St/yorl e
:




⑫
1 -
a + 0




van
I
& 21afz



I :
1 -




>
-




&3 Fats


2




↳
a = -




-



⑧ O




ophern :


&
( tit
1 a




te
4) ))
:



...




nelf

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August 31, 2026
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