- #1
bennyska
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Homework Statement
if T is a linear operator on V and dim V = 4 and charpoly(T)=t2(t-1)(t+7), then is T one-to-one? What is the dimension of the nullspace of T?
Homework Equations
The Attempt at a Solution
So i know T has 3 eigenvalues, 0, 1, -7. Since 0 is an eigenvalue, i know there's at least one vector v in V, v =! 0, such that T(v) = 0v = 0. so i know T is not one to one.
now i need to figure out the dimension of the null space. but i don't know anything about T, other than the charpoly splits. if i knew dim eigenspace corresponding to 0 = 2, then i would be able to construct a basis, and show that null space of T has dim 2. so, I'm a little lost.