Dieses Dokument bietet eine umfangreiche Sammlung von Aufgaben und Lösungen im Bereich der Matrizen, speziell konzipiert für Studierende im Bachelor of Engineering (B.Eng.) Studiengang. Matrizen sind ein grundlegendes Konzept in der linearen Algebra und spielen eine entscheidende Rolle in verschi...
Gegeben sind die Matrizen
0 1 0 1 0 1
2 7 5 0 3 1 2 1 3 4 2 1 3
B 1 3 0 4 1 C B 2 0 2 5 0 C B 0 3 0 C
B C B C B C
A=B C
B 5 2 3 5 0 C, B = B
B 4 3 7 5 2 C und C = B
C B 1 2 5 C.
C
@ 6 1 2 1 3 A @ 3 1 2 2 3 A @ 3 2 2 A
1 0 1 3 7 1 4 6 3 0 7 5 1
Zeigen Sie, dass A · C + B · C = (A + B) · C gilt.
2. Aufgabe
Gegeben sind die Matrizen
0 1 0 1
1 1 0 ✓ ◆ 1 4 2
1 4 2
A = @ 2 3 5 A, B = , C=@ 0 1 1 A
4 0 3
0 1 4 3 2 5
✓ ◆
1 0
und D = .
0 1
Ergebnisse:
a) D = 0 b) D = 640 c) D = 96 d) D = 24
Wiederholung Komplexe Zahlen:
Alte Klausuraufgabe
p !
2 3 5i 3 p
Gegeben ist die komplexe Zahl z = p 3 3i .
3 3+i
a) Berechnen Sie Real- und Imaginärteil von z.
⇡
b) Berechnen Sie alle Lösungen w 2 C der Gleichung w3 + i · ei 2 = 0 und geben
Sie diese in kartesischer Form an.
Ergebnisse:
p 1 1p 1 1p
a)z = 3 i5 b) w0 = 1, w1 = +i 3, w2 = i 3
2 2 2 2
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