I'm not really sure with this question because whenever these kinds of problems appears, it always comes with an integrals definition of the inner product but this time we are only given this:
$$ x(t) = x_{1}t^{2} + x_{1}t + x_{0} $$ $$ y(t) = y_{1}t^{2} + y_{1}t + y_{0} $$
in P2[t], defined $$ <x(t),y(t)> = x_{2}y_{2} + x_{1}y_{1} + 3x_{0}y_{0} $$
Then the question is that if $ x(t) = t^{2}-2, y(t) = t+1,s(t)= 3t^{2} -t$
compute for $||x(t)||$. What do I do with the the definition of $<x(t),y(t)>$ to solve this probem? Or i dont think for this problem? I'm thinking of writing x(t) in coordinate vectors by using a standard basis for P2[t] then from that solve the length using this: enter image description here
Edit: I just realized the image I attached above is the dot product.
By the definition of the norm of an inner-product space,
$\|p(t)\| = \sqrt{\langle p(t),p(t)\rangle}$.