Problem Set 3: LU decomposition, Vector spaces and linear independence
 Due Oct 26, 2016 by 5pm
 Points 20
 Submitting a file upload
 File Types pdf
 Available after Oct 19, 2016 at 3:30pm
This assignment has coding (20 pts) and written (20 pts) parts. Upload written parts as a pdf here. Submit your code to scorelator.
Quiz 2 will ask questions about this assignment. You may want to start Quiz 2 while you work through the assignment.
Here is the problem set: ProblemSet3.pdf and you will also need this .m file: GE_NEW.m
(note that GE_NEW is not the same as GE_NMM from last time).
There is no new video tutorial for this problem set. Please use office hours or the Discussion board if you need help Discussion Module 3: (PS3) LU decomposition, Vector Spaces and Linear Independence
Clarification: For problems 2.3 (d) and (e), $\mathbb{P}$ refers to the space of all polynomials.
For problem 2.2. Here, I was using ${\mathbb{R}}^{2}$ and ${\mathbb{R}}^{3}$ to refer to the physical spaces. ${\mathbb{R}}^{2}$ can considered a subset of ${\mathbb{R}}^{3}$ if it is represented using $\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\\ 0\end{array}\right]$. Sometimes ${\mathbb{R}}^{2}$ is used to refer to the set of all 2 component vectors. I am not using it in that sense. I will try to be more clear which sense I mean it in the future. If you take it to mean all 2 component vectors, we will grade you based on that assumption.
Rubric
Criteria  Ratings  Pts  

2.1 (a) Demonstrate all 10 conditions and conclude it is a vector space.
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2.1 (b) Demonstrate that it is not a vector space by showing one of ten conditions is not satisfied.
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2.2 (i) Show why W is not a subspace.
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2.2 (ii) Show W is a subspace
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2.3 (a) The set is linearly dependent
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2.3 (b) The set is linearly dependent
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2.3 (c) The set is linearly independent
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2.3 (d) The set is linearly independent
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2.3 (e) The set is linearly independent
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Total Points:
20.0
out of 20.0
