14-240/Tutorial-November4: Difference between revisions

Revision as of 11:56, 29 November 2014

#	Week of...	Notes and Links
Welcome to Math 240! (additions to this web site no longer count towards good deed points)
1	Sep 8	About This Class, What is this class about? (PDF, HTML), Monday, Wednesday
2	Sep 15	HW1, Monday, Wednesday, TheComplexField.pdf,HW1_solutions.pdf
3	Sep 22	HW2, Class Photo, Monday, Wednesday, HW2_solutions.pdf
4	Sep 29	HW3, Wednesday, Tutorial, HW3_solutions.pdf
5	Oct 6	HW4, Monday, Wednesday, Tutorial, HW4_solutions.pdf
6	Oct 13	No Monday class (Thanksgiving), Wednesday, Tutorial
7	Oct 20	HW5, Term Test at tutorials on Tuesday, Wednesday
8	Oct 27	HW6, Monday, Why LinAlg?, Wednesday, Tutorial
9	Nov 3	Monday is the last day to drop this class, HW7, Monday, Wednesday, Tutorial
10	Nov 10	HW8, Monday, Tutorial
11	Nov 17	Monday-Tuesday is UofT November break
12	Nov 24	HW9
13	Dec 1	Wednesday is a "makeup Monday"! End-of-Course Schedule, Tutorial
F	Dec 8	The Final Exam
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Let $a\in R$ and $W=\{f\in P_{n}(R):f(a)=0\}$ be a subspace of $P_{n}(R)$ . Find $dim(W)$ .

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

@@ Line 5: / Line 5: @@
 ====Question 26 on Page 57 in Homework 5====
-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>.
 There are several approaches to this problem.