[線代] linear transformation (onto)

[mqazz1 (無法顯示)]

a linear transformation L: V -> W is said to map V onto W if L(V)=W

show that the linear transformation L defined by

L(x) = ( x1, x1+x2, x1+x2+x3 )^T

maps R^3 onto R^3


請問這題要怎麼證呢?

謝謝!!

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→ ricestone   :你就證明R^3所有向量都能寫成某組(x1,x2,x3)被L的解
→ psistorm    :更明確的說你只要證明 L(x)=[1,0,0], L(x)=[0,1,0]
→ psistorm    :L(x)=[0,0,1] 都有解
推 suzzdicon   :Dimension Thm
推 zombiea     :check injective, this is Linear algebra