Álgebra linear Exemplos

Problemas populares
Álgebra linear
Ermittle das Ergebnis von 5 mal der 5x5-Einheitsmatrix 5
55
Etapa 1
A matriz identidade ou matriz unitária de tamanho 55 é a matriz quadrada 5×55×5 com números "um" na diagonal principal e zeros nos outros lugares.
[1000001000001000001000001]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1000001000001000001000001⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Etapa 2
Multiply the scalar 55 by the identity matrix.
5[1000001000001000001000001]5⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1000001000001000001000001⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Etapa 3
Simplifique.
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Etapa 3.1
Multiplique 55 por cada elemento da matriz.
[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⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Etapa 3.2
Simplifique cada elemento da matriz.
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Etapa 3.2.1
Multiplique 55 por 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⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Etapa 3.2.2
Multiplique 55 por 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⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Etapa 3.2.3
Multiplique 55 por 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⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Etapa 3.2.4
Multiplique 55 por 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⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Etapa 3.2.5
Multiplique 55 por 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⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Etapa 3.2.6
Multiplique 55 por 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⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Etapa 3.2.7
Multiplique 5 por 1.
[50000055⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Etapa 3.2.8
Multiplique 5 por 0.
[500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Etapa 3.2.9
Multiplique 5 por 0.
[5000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Etapa 3.2.10
Multiplique 5 por 0.
[50000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Etapa 3.2.11
Multiplique 5 por 0.
[500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Etapa 3.2.12
Multiplique 5 por 0.
[5000005000005⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Etapa 3.2.13
Multiplique 5 por 1.
[50000050000055⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Etapa 3.2.14
Multiplique 5 por 0.
[500000500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Etapa 3.2.15
Multiplique 5 por 0.
[5000005000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Etapa 3.2.16
Multiplique 5 por 0.
[50000050000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Etapa 3.2.17
Multiplique 5 por 0.
[500000500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Etapa 3.2.18
Multiplique 5 por 0.
[5000005000005000005⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Etapa 3.2.19
Multiplique 5 por 1.
[50000050000050000055⋅05⋅05⋅05⋅05⋅05⋅1]
Etapa 3.2.20
Multiplique 5 por 0.
[500000500000500000505⋅05⋅05⋅05⋅05⋅1]
Etapa 3.2.21
Multiplique 5 por 0.
[5000005000005000005005⋅05⋅05⋅05⋅1]
Etapa 3.2.22
Multiplique 5 por 0.
[50000050000050000050005⋅05⋅05⋅1]
Etapa 3.2.23
Multiplique 5 por 0.
[500000500000500000500005⋅05⋅1]
Etapa 3.2.24
Multiplique 5 por 0.
[5000005000005000005000005⋅1]
Etapa 3.2.25
Multiplique 5 por 1.
[5000005000005000005000005]
[5000005000005000005000005]
[5000005000005000005000005]
 [x2  12  √π  ∫xdx ]