14-240/Tutorial-November11

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

Coordinate and Matrix Representation Problems

Recall:

Let $V$ be a finite dimensional vector space over a field $F$, $B={v_{1},v_{2},v_{3},...,v_{n}}$ be an ordered basis of $V$ and $v\in V$. Then $v=\displaystyle \sum _{i=1}^{n}c_{i}v_{i}$ where $c_{i}\in F$. Then the coordinate representation of $v$ is the column vector \begin{pmatrix}c_1\\c_2\\c_3\\.\\c_n\end{pmatrix}</math>.

Let $W$ be a finite dimensional vector space over the same field $F$, $B={v_{1},v_{2},v_{3},...,v_{m}}$ be an ordered basis of $W$. Define a linear transformation $T:V\to W$. Then the matrix representation of $T$ in the ordered bases $B,K$ is the matrix