Question

asked 2020-11-30

Consider \(\displaystyle{V}={\cos{{\left({x}\right)}}},{\sin{{\left({x}\right)}}}\) a subspace of the vector space of continuous functions and a linear transformation \(\displaystyle{T}:{V}\rightarrow{V}\) where \(\displaystyle{T}{\left({f}\right)}={f{{\left({0}\right)}}}\times{\cos{{\left({x}\right)}}}−{f{{\left(π{2}\right)}}}\times{\sin{{\left({x}\right)}}}.\)

Find the matrix of T with respect to the basis \(\displaystyle{\cos{{\left({x}\right)}}}+{\sin{{\left({x}\right)}}},{\cos{{\left({x}\right)}}}−{\sin{{\left({x}\right)}}}\) and determine if T is an isomorphism.

asked 2021-03-02

asked 2021-03-02

asked 2021-01-02