According to the textbook we use, $$F$$ is a field over $$\Bbb{R}$$ or $$\Bbb{C}$$. $${P}_{m}(F)$$ is the polynomial space of degree m.
One of the many problem with my homework is indeed the handwriting, my professor is not very consistent with his upper and lower case letters. I just copied...
I not very good at using the LaTex editor, so I took a photo of my HW questions.
For the first question, I'm not really sure how to get started, should I write out a specific case? Like what would $$\varphi (P)$$ be when m=1?
For the second question, I know that a linear functional have two...