(6) Suppose that T is a linear operator on a 2 dimensional vector space V and that T+ a I for any a e F. Then if U E L(V) and UT = TU then U = g(T) for some polynomial g(x).
(6) Suppose that T is a linear operator on a 2 dimensional vector space V and that T+ a I for any a e F. Then if U E L(V) and UT = TU then U = g(T) for some polynomial g(x).
(6) Suppose that T is a linear operator on a 2 dimensional vector space V and that T+ a I for any a e F. Then if U E L(V) and UT = TU then U = g(T) for some polynomial g(x).
6) Suppose that ? is a linear operator on a 2 dimensional vector space ? and that ? = ̸ ? ? for any ? ∈ F. Then if ? ∈ L(V) and ?? = ?? then ? = ?(?) for some polynomial ?(?)
Transcribed Image Text:(6) Suppose that \( T \) is a linear operator on a 2-dimensional vector space \( V \) and that \( T \neq aI \) for any \( a \in \mathbb{F} \). Then if \( U \in \mathcal{L}(V) \) and \( UT = TU \) then \( U = g(T) \) for some polynomial \( g(x) \).
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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