14-240/Tutorial-November4

DBN: Classes: 2014-15: 14-240 / Navigation Welcome to Math 240! (additions to this web site no longer count towards good deed points) # Week of... Notes and Links 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 Register of Good Deeds Add your name / see who's in!

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 without Decomposing the Polynomial