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n = 4 (λ−t) 4 4 4 = 3 + 1 = 2 + 2 = 2 + 1 + 1 = 1 + 1 + 1 + 1 <br />
<br />
⎛<br />
⎞ ⎛<br />
⎞ ⎛<br />
⎞<br />
λ 1<br />
λ 1<br />
λ<br />
⎟<br />
1⎠<br />
λ<br />
⎜<br />
⎝<br />
(λ − t) 4<br />
⎛<br />
λ 1<br />
⎜<br />
⎝<br />
λ<br />
(λ − t) 2<br />
λ<br />
λ<br />
⎞<br />
⎟<br />
⎠<br />
⎜<br />
⎝<br />
λ 1<br />
(λ − t) 3<br />
⎛<br />
λ<br />
⎜ λ<br />
⎝<br />
λ − t<br />
λ 1<br />
λ<br />
n((α − λι) r ) r <br />
<br />
⎛<br />
2 0 0<br />
⎞<br />
0<br />
⎜<br />
A = ⎜3<br />
⎝0<br />
2<br />
0<br />
0<br />
2<br />
−2 ⎟<br />
0 ⎠<br />
0 0 2 2<br />
χA(t) = (2 − t) 4 <br />
⎛<br />
0 0 0<br />
⎞<br />
0<br />
⎜<br />
A − 2I = ⎜3<br />
⎝0<br />
0<br />
0<br />
0<br />
0<br />
−2 ⎟<br />
0 ⎠<br />
0 0 2 0<br />
λ<br />
λ<br />
λ<br />
⎟<br />
⎠<br />
⎞<br />
⎟<br />
⎠<br />
⎜<br />
⎝<br />
λ 1<br />
λ<br />
(λ − t) 2<br />
⎟<br />
λ 1⎠<br />
λ<br />
(A − 2I) 2 ⎛<br />
0 0 0<br />
⎞<br />
0<br />
⎜<br />
= ⎜0<br />
⎝0<br />
0<br />
0<br />
−4<br />
0<br />
0 ⎟<br />
0⎠<br />
0 0 0 0<br />
A mA(t) = (2 − t) 3 n(A − 2I) = 2 <br />
A <br />
⎛<br />
2 1 0<br />
⎞<br />
0<br />
⎜<br />
JNF = ⎜0<br />
⎝0<br />
2<br />
0<br />
1<br />
2<br />
0 ⎟<br />
0⎠<br />
0 0 0 2<br />
.<br />
v3 ∈ ker(A − 2I) 2 v3 = (0, 0, 1, 0) T A − 2I<br />
⎛ ⎞<br />
0<br />
⎜<br />
v3 = ⎜0<br />
⎟<br />
⎝1⎠<br />
0<br />
↦→ v2<br />
⎛ ⎞<br />
0<br />
⎜<br />
= ⎜0<br />
⎟<br />
⎝0⎠<br />
2<br />
↦→ v1<br />
⎛ ⎞<br />
0<br />
⎜<br />
= ⎜−4<br />
⎟<br />
⎝ 0 ⎠ ↦→ 0.<br />
0<br />
v4 v4 = (2, 0, 0, 3) T
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