14-240/Tutorial-November4

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Boris

Question 26 on Page 57 in Homework 5

Let [math]\displaystyle{ a \in R }[/math] and [math]\displaystyle{ W = {f \in P_n(R): f(a) = 0} }[/math] be a subspace of [math]\displaystyle{ P_n(R) }[/math]. Find [math]\displaystyle{ dim(W) }[/math].

There are several approaches to this problem.

Approach 1: Use Isomorphisms

Approach 2: Use the Rank-Nullity Theorem

Approach 3: Find a Basis by Decomposing the Polynomial

Approach 4: Find a Basis of without Decomposing the Polynomial