Suppose vectors V_i , ( i = 1,2,...,p )
span R^n , and let T: R^n --> R^n be the linear transformation.
Suppose T(vi) = 0 , for i = 1,2,...,p
show that T is a zero transformation
that is show that if x is any vector on R^n , then T( x)=0
UST Maths problem
2009-10-07 11:27 pm
回答 (1)
2009-10-08 12:54 am
✔ 最佳答案
Since v_i's span R^n. So for any vector x in R^n, it can be represented as x=a_1v_1+a_2v_2+...+a_nv_nT(x)=T(a_1v_1+a_2v_2+...+a_nv_n)
=a_1T(v_1)+a_2T(v_2)+...+a_nT(v_n)
=0
We have just shown that if x is any vector on R^n. Then T( x)=0
收錄日期: 2021-04-26 14:02:59
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091007000051KK00637