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Komplette Abiturzusammenfassung Lineare Algebra
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Matheklausur Q2.1Lineare Gleichungssysteme
Anzahl Variablen
Normalform" 3 +
2y 2z 1
=
X
-
↓
Überbestimmtes LGS
d 4 .
.
alle Summanden mit 2x +
3y
T
2z -
14
(3) -
LGS
=
mehr Gl .
als Variablen
links 4
2y 3z g Anzahl
- I
Variablen
·
alle ohne X -
Gl .
,
rechts des Gleichheitszeichen 5x -
4y -
42 I
1
-
Aquivalenzumformungen eines GIS
Gauß-Verfahren
.
1 2 tauschen
Gleichungen .
1 Forme das LGS in obere
Dreiecksform um
mit Zahl KF O
.
2 eine
Gleichung einer
r eellen multipl .
.
2 Lösen der #I .
Gleichung und
Rückeinsetzung
.
3 Gl
eine
Gleichung zu einer anderen .
addieren nach oben
3x +
3y + 2z =
5
obere Dreiecksform :
by + 5z = 2
Interpretation Ergebnis Z -
2
1) Widerspruch/falsche Aussage
↓ =
Ei gibt keine
Lösung
Geraden sind echt
parallel Koeffizientenmatrix
2) eindeutige Lösung x +
y-
z = 5 1 T 1 -
1 +
5
↓ 4x ; =
z -
3 +
2y + 3 z =.
5 => te 3 +
2 +
3 -
5
y :
-
2x 2
Geraden Punkt 2y & 2 2
=
treffen 2 1
+
sich in diesem
+
-
-
+
3) trivale Zeile (bsp .
0 = 0)
↓ R Umformung bis oo 3
unendlich viele
Lösungen 1
= -
;
Geraden sind identisch => 0 10 2
o O 1 O
3D - Zeichnen
Punkt mit Koordinaten :
010/0/0) wirdo"
genannt
Abstand Punkt im Raum
d V(x xx) yn)) zn))
(yz (zu
= -
+ +
- -
,
W4 a NICHT
Achtung bei die Wurzel ziehen !
: +
~ Summe !
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