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Homework Statement
i know how to find the basis of a subspace of R2 or R3 but I can't figure out how to find the basis of a subspace of something like R2,2.
I even have an example in my book which i managed to follow nearly till the end but not quite...
Given matrix:
A=
6 -9
4 -4
show that the subset F={X (of R2,2) | AX=XA } is a vector subspace of R2,2 and find its basisX =
x1 x1
x3 x4
Homework Equations
The Attempt at a Solution
I followed the example through by multiplying the matrices in the eq AX-XA=0 and found the solution for the associated system of equations which after reducing it is:
4*x1 - 12*x3 - 4*x4 = 0
9*x1 +12*x2 - 9*x4 = 0
so:
x1 = 3*x3 + x4
x2 = -9/4*x3
x3 = x3
x4 = x4
then the example just says:
therefore the dimension of subset F is 2 and the basis are the 2 matrices:
12 -9
4 0
and
0 1
1 0
I don't know where these numbers come from please help.
I looked through the book and it only shows how to find basis for Rn but not Rn,n