So here is a question on linear transformations. Let L: P2--P2 be the linear transformation defined by L(at^2+bt+c)=(a+c)t^2+(b+c)t. Is 2t^2-1 in range of L? How would you go about solving it?

Question

So here is a question on linear transformations. Let L: P2-->P2 be the linear transformation defined by L(at^2+bt+c)=(a+c)t^2+(b+c)t. Is 2t^2-1 in range of L? How would you go about solving it?

myininaya · Answer

no i would say
your outputs are in the form of some constant times t^2+some constant times t
and you are asked is 2t^2-1 in the range
from this linear transformation we can not just get a constant