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Lineare Algebra Beispiele
55
Schritt 1
Die Identitätsmatrix oder Einheitsmatrix der Größe 55 ist die 5×55×5 Quadratmatrix mit Einsen auf der Hauptdiagonalen und Nullen überall anders.
[1000001000001000001000001]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣1000001000001000001000001⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Schritt 2
Multiply the scalar 55 by the identity matrix.
5[1000001000001000001000001]5⎡⎢
⎢
⎢
⎢
⎢
⎢⎣1000001000001000001000001⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Schritt 3
Schritt 3.1
Multipliziere 55 mit jedem Element der Matrix.
[5⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Schritt 3.2
Vereinfache jedes Element der Matrix.
Schritt 3.2.1
Mutltipliziere 55 mit 11.
[55⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣55⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Schritt 3.2.2
Mutltipliziere 55 mit 00.
[505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Schritt 3.2.3
Mutltipliziere 55 mit 00.
[5005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Schritt 3.2.4
Mutltipliziere 55 mit 00.
[50005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣50005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Schritt 3.2.5
Mutltipliziere 55 mit 00.
[500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Schritt 3.2.6
Mutltipliziere 55 mit 00.
[5000005⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5000005⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Schritt 3.2.7
Mutltipliziere 55 mit 11.
[50000055⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣50000055⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Schritt 3.2.8
Mutltipliziere 55 mit 00.
[500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Schritt 3.2.9
Mutltipliziere 55 mit 00.
[5000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣5000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Schritt 3.2.10
Mutltipliziere 55 mit 00.
[50000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣50000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Schritt 3.2.11
Mutltipliziere 55 mit 00.
[500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Schritt 3.2.12
Mutltipliziere 5 mit 0.
[5000005000005⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Schritt 3.2.13
Mutltipliziere 5 mit 1.
[50000050000055⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Schritt 3.2.14
Mutltipliziere 5 mit 0.
[500000500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Schritt 3.2.15
Mutltipliziere 5 mit 0.
[5000005000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Schritt 3.2.16
Mutltipliziere 5 mit 0.
[50000050000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Schritt 3.2.17
Mutltipliziere 5 mit 0.
[500000500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Schritt 3.2.18
Mutltipliziere 5 mit 0.
[5000005000005000005⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Schritt 3.2.19
Mutltipliziere 5 mit 1.
[50000050000050000055⋅05⋅05⋅05⋅05⋅05⋅1]
Schritt 3.2.20
Mutltipliziere 5 mit 0.
[500000500000500000505⋅05⋅05⋅05⋅05⋅1]
Schritt 3.2.21
Mutltipliziere 5 mit 0.
[5000005000005000005005⋅05⋅05⋅05⋅1]
Schritt 3.2.22
Mutltipliziere 5 mit 0.
[50000050000050000050005⋅05⋅05⋅1]
Schritt 3.2.23
Mutltipliziere 5 mit 0.
[500000500000500000500005⋅05⋅1]
Schritt 3.2.24
Mutltipliziere 5 mit 0.
[5000005000005000005000005⋅1]
Schritt 3.2.25
Mutltipliziere 5 mit 1.
[5000005000005000005000005]
[5000005000005000005000005]
[5000005000005000005000005]