Ma4A_ChAv2_ComplAlgLin_ChgmtBase

Saisir les vecteurs u et v en fonction de vecteurs i et j.
Déplacer le point rouge pour modifier le vecteur X quelconque.

Observer le lien entre les coorodonnées dans la base B et la base B' à l'aide de la multiplication par la matrice de passage.

v=-2 i+j

b_1=

b_2=

\textsf{Soient les bases C=} (\vec{i},\vec{j}) \textsf{et B=} (\vec{b_1},\vec{b_2}) \textsf{ telles que :}

\vec{v}

O = (0, 0)
J = (0, 1)
j = Vector(J)
I = (1, 0)
i = Vector(I)
liste1 = Sequence(Sequence[Translate[O, Vector[((0.5 * m) * i) + ((0.5 * n) * j)]], m, -20, 20], n, -20, 20)
b_1: (2 * i) + j
a = Line(O, i)
b = Line(O, j)
P = (2.9243409622710677, 2.4863068518729645)
c = Line(P, a)
d = Line(P, b)
A = Intersect(d, a)
B = Intersect(b, c)
Xi: (i * Vector[O, A] / ((i * i)))
Xj: (j * Vector[O, B] / ((j * j)))
U = Translate(O, b_1)
e = Line(U, b)
f = Line(U, a)
C = Intersect(f, b)
D = Intersect(e, a)
Ui: (i * Vector[O, D] / ((i * i)))
Uj: (j * Vector[O, C] / ((j * j)))
b_2: (0 * i) - j
V = Translate(O, b_2)
g = Line(V, b)
h = Line(V, a)
E = Intersect(a, g)
F = Intersect(h, b)
Vi: (i * Vector[O, E] / ((i * i)))
Vj: (j * Vector[O, F] / ((j * j)))
k = Line(O, U)
l = Line(O, V)
m = Line(P, k)
n = Line(P, l)
G = Intersect(n, k)
H = Intersect(m, l)
Xu: (b_1 * Vector[O, G] / ((b_1 * b_1)))
Xv: (b_2 * Vector[O, H] / ((b_2 * b_2)))
w = Vector(O, H)
q = Vector(O, G)
p = Segment(G, P)
r = Segment(P, H)
K = Midpoint(H, O)
L = Midpoint(G, O)
texte1: "" + Xu + "u"
texte2: "" + Xv + "v"
s = Segment(B, P)
t = Segment(A, P)
u_1 = Vector(O, A)
v_1 = Vector(O, B)
M = Midpoint(A, O)
N = Midpoint(B, O)
texte3: "" + Xi + "i"
texte4: "" + Xj + "j"
w_1 = Vector(O, P)
P_1 = Midpoint(O, P)
P_{2}: {{Ui, Vi}, {Uj, Vj}}
ChampTexte1 = Textfield(b_1)
ChampTexte2 = Textfield(b_2)
UB: {{Ui}, {Uj}}
VB: {{Vi}, {Vj}}
XB: {{Xi}, {Xj}}
matrice1: {{Xu}, {Xv}}
Q = Point(b_2)