Question

let v1,v2, v3 be vectors in vector space V, and let T:V--->R^3 be a linear transformation for which T(v1)=(1,-1,2),T(v2)=(0,3,2),T(v3)=(-3,1,2)
find T(2v1-3v2+4v3)
Help, please

Answer 1

ok, i got it by myself, just need check = (-10,-7,6)
and the steps are T(2v1 -3v2 +4v3) = T(2v1) +T(-3v2) + T(4v3)
= 2T(v1) -3T(v2) +4T(v3) = (2,-2,4) - (0,9,6)+-12,4,8) = (-10,-7,6)