Re: [理工] [線代]-Linear transformation

[chris750630 (何去何從？)]

※ 引述《gn00618777 (123)》之銘言：
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: Let T: R ---> R  be a linear transformation. Prove that,if
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: T(T(x))=T(x)+T(x)+3x,for all x 屬於R , Then T is one to one
:             n       n
: mapping of R  into R

Suppose T be not 1-1 ,so exist a,b&y (-R^n s.t T(a)=T(b)=y =>a!=b

T(T(a))=T(y)=T(T(b))=T(a)+T(a)+3a=T(b)+T(b)+3b => OMG! a=b

所以假設矛盾 QED

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我絕對不會說 這是我的無名.........

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推 gn00618777:唔-.- 了解了..