- #1
Saladsamurai
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Homework Statement
Find the eigen values, eigenspaces of the following matrix and also determine a basis for each eigen space for A = [1, 2; 3, 4]
Homework Equations
[itex]\det(\mathbf{A} - \lambda\mathbf{I}) = 0[/itex]
The Attempt at a Solution
OK, so I found the eigenvalues and eigenspaces just fine. For eigen values I found [itex]\lambda_{1,2} = -0.372, 5.372}[/itex] which matches the answer in text. I also found that e1 = [-1.457, 1]T and e2 = [0.4575, 1]T which is also correct.
It is this "basis" thing that I am not understanding. Please keep in mind this is an engineering advanced math methods course, so though I do know about matrix operations, I am by no means a linear algebra wizard over here.
Upon looking up the definition of a basis, it seems that it is just a set of linearly independent (LI) vectors that can be used to write all of the other vectors in that particular set in terms of (i.e. as linear combinations of). OK great. So a set {u1, u2} in a vector space S is a basis for S iff u1 and u2 are LI. And apparently the set needs to "span S" too (still working on what that means).
So I guess what my big question is, is what is my S for which I am trying to find basises (spelling?) for? How do I start this?
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