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Algèbre linéaire Exemples
55
Étape 1
La matrice d’identité ou matrice d’unité de taille 55 est la matrice carrée 5×55×5 avec les uns sur la diagonale principale et les zéros ailleurs.
[1000001000001000001000001]⎡⎢
⎢
⎢
⎢
⎢
⎢⎣1000001000001000001000001⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Étape 2
Multiply the scalar 55 by the identity matrix.
5[1000001000001000001000001]5⎡⎢
⎢
⎢
⎢
⎢
⎢⎣1000001000001000001000001⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Étape 3
Étape 3.1
Multipliez 55 par chaque élément de la matrice.
[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⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Étape 3.2
Simplifiez chaque élément dans la matrice.
Étape 3.2.1
Multipliez 55 par 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⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Étape 3.2.2
Multipliez 55 par 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⎤⎥
⎥
⎥
⎥
⎥
⎥⎦
Étape 3.2.3
Multipliez 5 par 0.
[5005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.4
Multipliez 5 par 0.
[50005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.5
Multipliez 5 par 0.
[500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.6
Multipliez 5 par 0.
[5000005⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.7
Multipliez 5 par 1.
[50000055⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.8
Multipliez 5 par 0.
[500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.9
Multipliez 5 par 0.
[5000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.10
Multipliez 5 par 0.
[50000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.11
Multipliez 5 par 0.
[500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.12
Multipliez 5 par 0.
[5000005000005⋅15⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.13
Multipliez 5 par 1.
[50000050000055⋅05⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.14
Multipliez 5 par 0.
[500000500000505⋅05⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.15
Multipliez 5 par 0.
[5000005000005005⋅05⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.16
Multipliez 5 par 0.
[50000050000050005⋅05⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.17
Multipliez 5 par 0.
[500000500000500005⋅05⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.18
Multipliez 5 par 0.
[5000005000005000005⋅15⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.19
Multipliez 5 par 1.
[50000050000050000055⋅05⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.20
Multipliez 5 par 0.
[500000500000500000505⋅05⋅05⋅05⋅05⋅1]
Étape 3.2.21
Multipliez 5 par 0.
[5000005000005000005005⋅05⋅05⋅05⋅1]
Étape 3.2.22
Multipliez 5 par 0.
[50000050000050000050005⋅05⋅05⋅1]
Étape 3.2.23
Multipliez 5 par 0.
[500000500000500000500005⋅05⋅1]
Étape 3.2.24
Multipliez 5 par 0.
[5000005000005000005000005⋅1]
Étape 3.2.25
Multipliez 5 par 1.
[5000005000005000005000005]
[5000005000005000005000005]
[5000005000005000005000005]