So here is a theoretical question. Let L1 and L2 be linear transformation from a vector space V into Vector space W. Let {v1,v2,

Question

Anon25 [30]

2 years ago

9

So here is a theoretical question. Let L1 and L2 be linear transformation from a vector space V into Vector space W. Let {v1,v2,

....,vn} be a basis for V. Show that if L1(vi)=L2(vi) for i=1,2,....,n then L1(v)=L2(v) for any v in V. ...?

Mathematics

1 answer:

noname [10] · Answer 1 · 2022-08-31T12:30:21+03:00

noname [10]2 years ago

6 0

<span>if v belongs to V, then we can find scalars a1,a2,...,an, such that v=a1*v1+a2*v2+...+an*vn, L1(v)=L1(a1*v1+a2*v2+...+an*vn) =a1*L1(v1)+a2*L1(v2)+...+an*L1(vn) =a1*L2(v1)+a2*L2(v2)+...+an*L2(vn) =L2(a1*v1+a2*v2+...+an*vn) =L2(v)</span>