14-240/Tutorial-November4: Difference between revisions
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====Question 26 on Page 57 in Homework 5==== |
====Question 26 on Page 57 in Homework 5==== |
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Let <math>a \in R</math> and <math>W = {f \in P_n(R): f(a) = 0}</math> be a subspace of <math>P_n(R)</math>. Find <math>dim(W)</math>. |
Let <math>a \in R</math> and <math>W = \{f \in P_n(R): f(a) = 0\}</math> be a subspace of <math>P_n(R)</math>. Find <math>dim(W)</math>. |
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There are several approaches to this problem. |
There are several approaches to this problem. |
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Revision as of 10:56, 29 November 2014
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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
