Let α={e1=(1,0,0),e2=(0,1,0),e3=(0,0,1)} be the canonical basis of R3 and consider the linear operator T:R3→R3 that satisfies T(e1)=3e1+e3 T(e2)=2e2 T(e3)=2e2−e3 It is correct to say that: a) The characteristic polynomial of T is p(λ)=−(2−λ)(3−λ)(1+λ) and the eigenspaces V−1, V2 and V3 of
Let α={e1=(1,0,0),e2=(0,1,0),e3=(0,0,1)} be the canonical basis of R3 and consider the linear operator T:R3→R3 that satisfies
T(e1)=3e1+e3
T(e2)=2e2
T(e3)=2e2−e3
It is correct to say that:
a) The characteristic polynomial of T is p(λ)=−(2−λ)(3−λ)(1+λ) and the eigenspaces V−1, V2 and V3 of T satisfy dim(V−1)+dim(V1)+dim(V3)=3.
b) The eigenvalues of T are −1, 2 and 3 and the eigenspaces V−1, V2 and V3 of T satisfy dim(V−1)⋅dim(V1)⋅dim(V3)=3.
c) The eigenvalues of the operator T are −1, 2 and 3 and the eigenspaces V−1, V2 and V3 of T satisfy dim(V−1)+dim(V1)+dim(V3)=2.
d) The characteristic polynomial of T is p(λ)=−(2−λ)(3−λ)(1+λ) and the eigenspaces V−1, V2 and V3 of T satisfy dim(V−1)+dim(V1)+dim(V3)=2.
e) The eigenvalues of operator T are 0, 2 and 3 and the eigenspaces V0, V2 and V3 of T satisfy dim(V0)+dim(V1)+dim(V3)=3.
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