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Finding a Transformation Matrix to yield the basis

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silvermane
#1
Oct5-10, 11:08 PM
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1. The problem statement, all variables and given/known data
The solutions to the linear differential equation d^2u/dt^2 = u for a vector space. Find two independent solutions, to give a basis for that solution space.

3. The attempt at a solution
I want to understand this question. I feel that there's something I'm missing. I believe that I need to find the Transformation Matrix, but I need to understand how :(

Any hints or tips are greatly appreciated, but please don't give me just an answer! :)))
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hgfalling
#2
Oct5-10, 11:18 PM
P: 351
I don't really think you're looking for a transformation matrix here. You have some vector space, with a vector u. There are a bunch of vectors (an infinite number, in fact!) in the space that solve the equation [itex] u'' = u [/itex]. What you want is a way to write down any vector that solves that equation as the sum of two other vectors (that you are going to find).

Now, what vectors solve this equation?
silvermane
#3
Oct5-10, 11:30 PM
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P: 117
Well now... I feel like a noob :D

e^t and e^-t are a basis... I misread the question -.-


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