題組內容

3. Let T : R4 →R4 be the linear map defined by 
T(a, b,c,d) = (a + 2d, b - 2c, -2b + c, 2a + d) 
Let β={e1,e2,e3,e4} be the standard ordered basis for R4 (for example, e1 = (1,0,0,0)).

b. (5pts) Find the minimal polynomial m(x) of T. Explain why your answer is indeed 
 minimal.
Hint: by defnition, m(x) is the monic non-zero polynomial with smallest degree such that m(T) is the zero map onR4.

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a. (5pts) Find the characteristic polynomial of T.
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