作者mqazz1 (无法显示)
看板Math
标题[线代] linear transformation (onto)
时间Sat May 14 22:22:37 2011
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
请问这题要怎麽证呢?
谢谢!!
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1F：→ ricestone :你就证明R^3所有向量都能写成某组(x1,x2,x3)被L的解 05/14 22:30
2F：→ psistorm :更明确的说你只要证明 L(x)=[1,0,0], L(x)=[0,1,0] 05/14 22:44
3F：→ psistorm :L(x)=[0,0,1] 都有解 05/14 22:45
4F：推 suzzdicon :Dimension Thm 05/15 03:38
5F：推 zombiea :check injective, this is Linear algebra 05/15 19:47