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ejercicio de albegra lineal, sistema de ecuaciones y solución por metodo grafico y analitico
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Ejercicio 1: Axiomas en un Espacio Vectorial. Realice la verificación de los siguientes axiomas del
espacio vectorial ℝ𝟑 utilizando los escalares y los vectores proporcionados.
B. Vectores: 𝒖⃗ = (𝟒, 𝟐, −𝟏); 𝒗⃗ = (−𝟑, −𝟓, 𝟔) y 𝒘⃗ = (𝟔, 𝟏, 𝟐).
Escalares: 𝜆=3; β=4.
Cerradura bajo la suma de vectores: 𝑺𝒊 𝒖⃗ , 𝒗⃗ ϵ 𝐑
𝟑
, 𝒆𝒏𝒕𝒐𝒏𝒄𝒆𝒔 𝒖⃗ + 𝒗⃗ 𝛜 𝐑
3
⃗ u + ⃗ v =( 4 , 2 , − 1 ) +(− 3 , − 5 , 6 )=( 4 − 3 , 2 − 5 , − 1 + 6 )
u ⃗ + ⃗ v =
es un vector preteneciente a R
3
Cerradura bajo el producto escalar: 𝑺𝒊 𝛌ϵ 𝐑 y 𝒖⃗ ϵ , 𝒆𝒏𝒕𝒐𝒏𝒄𝒆𝒔 𝛌𝒖⃗ 𝛜 𝐑
𝟑
λ u = 3 ( 4 , 2 , − 1 )=( 12 , 6 , − 3 ) es un vector que pertenece a R
3
Asociatividad de la suma: 𝒖⃗ + (𝒗⃗ + 𝒘⃗ ) = (𝒖⃗ + 𝒗⃗ ) + 𝒘⃗.
u ⃗ +( ⃗ v + ⃗ w )=( u ⃗ + ⃗ v ) + ⃗ w
⃗ u +(− ⃗ u )=(− u ⃗ ) + ⃗ u
Conmutatividad de la suma: 𝒖⃗ + 𝒗⃗ = 𝒗⃗ + 𝒖⃗
⃗ u + ⃗ v = ⃗ v + ⃗ u