Question
(b) Let v, 2,... , vn be a basis of a vector space V. Suppose f: V -> V is a lincar map
so that
Vi -1 if 1 < i < m,
f(v)
if m
< in
where 1m < n and vo = 0.
(b.1) Find the matrix and the characteristic polynomial of f.
(b.2) Find a basis for the eigenspace of A = 1.
1)m is the minimal polynomial of f
(b.3) Show that (X
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Transcribed Image Text

(b) Let v, 2,... , vn be a basis of a vector space V. Suppose f: V -> V is a lincar map so that Vi -1 if 1 < i < m, f(v) if m < in where 1m < n and vo = 0. (b.1) Find the matrix and the characteristic polynomial of f. (b.2) Find a basis for the eigenspace of A = 1. 1)m is the minimal polynomial of f (b.3) Show that (X

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