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mmcgirr4
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Homework Statement
So the question is a map T: R^2x2 ---> R^2x2 by T(A) = BAB, where B = (1 1)
(1 1)
so i made A = (a c) and T(A) = ((a+b) + (c+d) (a+b) + (c+d))
(b d) ((a+b) + (c+d) (a+b) + (c+d))
now it asks Find a basis for the kernel of T and compute the dimension of the kernel T.
Homework Equations
The Attempt at a Solution
This is what I have, but I am not quite sure its right.
ker(T) = {VεR^2x2 : T (V) = 0(vector) R^2x2}
= {(a c) : [(a+b) + (c+d) (a+b) + (c+d)] = [0 0] }
{(b d) [a+b) + (c+d) (a+b) + (c+d)] [0 0] }
then
a = -b -c -d
b = -a-c-d
c = -a-b-d
d = -a-b-c
therefor the Ker(T) = {(a c) : a, b, c, d ε R^2x2}
{(b d) }
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