Linearviii_3

  u = (1,2,3,4) v = (4,3,2,1)    u = (1,3,−1,4) v = (3,8,−5,7) w = (2,9,4,23)    u = (1,−2,4,1) v = (2,1,0,−3) w = (3,−6,1,4) BB’ B B’

  uv w   e2 B P2  uv   u1 ,..., u n F1 F2 F1 F2 F1 F2   IR 3 u v w   u v w ∈ IR 3 IR 3 IR 3

      u + v − 2w u − v − w u + w

B e1

F1 = {( x, y, z ) / x = y = z} F2 = {(0, y , z )}

IR = F1 ⊕ F2 3

x + 3 y + 2z = 0  x + 5 y + z = 0 3 x + 5 y + 8 z = 0 

 x + 2 y − 2 z − 2s − t = 0   x + 2 y − z + 3s − 2t = 0 2 x + 4 y − 7 z + s + t = 0 

Funções Reais Linearmente IndependentesF

h( x) = 0 f (x) g (x) a ⋅ f ( x) + b ⋅ g ( x)

h(x) ∀x ∈ a b f ( x) = sen x g ( x) = cos x a e b a ⋅ sen x + b cos x = h( x ) π sen 0 = 0 cos 0 = 1 b a 2 f ( x) = sen x g ( x) = x f ( x) = cos x g ( x) = e x f ( x) = x 2 g ( x) = e x l ( x ) = sen x