A First Course in Linear Algebra · Problem SLT-C29

Linear Transformations — Robert Beezer

Mathematics — Linear Algebra · range-surjective-linear-transformations

Problem

Let

T: P_2 \to P_4

be given by

T(p(x)) = x^2 p(x)

. Find a basis of

\mathcal{R}(T)

. Is

T

surjective?