alglinear.py

Created by famille-bvc

Created on June 10, 2022

901 Bytes


exemple matrice :
  
       (2 -1  0)
mat(f)=(-6 3  0)
       (-4 2  2)

rang : 
rank([[2,-1,0],[-6,3,0],[-4,2,2]])

base du noyau : 
ker([[2,-1,0],[-6,3,0],[-4,2,2]])
-> prendre la premiere ligne et
la passer en colonne

image d'une matrice:
image([[2,-1,0],[-6,3,0],[-4,2,2]])

Montrer que f est endormophisme
faire le det, si != 0
=> f est un antomorphisme

correxion exo 

e1 = ([[1],[0]])
e2 = ([[0],[1]])

[u1]E = ([[-2],[3]])
[u2]E = ([[4],[-5]])

matrice de passage 

-> inverse de la matrice u 

mat(u)=[u1]E = ([[-2,3],[4,-5]])

------------------------

modulo:
powmod(a,n,m)
a^n(mod m) -> inverse => n=-1

ex :
  
resoudre 17x ≡ 15[26]

1) inverse de 17 ≡ 1[26]
powmod(17,-1,26) = -3

2) on multiplie 17 et 15 par -3
-3*17x ≡ -3*15[26]

3) on note x ≡ -45 ≡ 7[26]
               (a)  (b)
               
(a) => -3*15 = -45
(b) => (-3*15)-(-3*17)+1
    => (-45)-(-51)+1 = 7

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