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1. (15©) f(x), g(x) ∈ P [x], f(x) = 0, y²e ^‡ d:
(1) f(x) | g(x);
(2) ∀k ∈ N ¦ fk
(x) | gk
(x);
(3) •3g,êm ¦ fm
(x) | gm
(x).
2. (20©) (1) ¦n × nŒ_Ý T =
t1
t2
...
tn
_.
(2) ®•A = (aij)•˜‡n × nÝ , T Xþ¤«, t1 = t2 = · · · = tn =
1. Á¦T −1
AT .
3. (20©) éλ ØÓ Š äe •§|´Äk)§k)ž¦ÑÙ Ü)µ
λx1 + x2 + x3 = λ + 1,
x1 + λx2 + x3 = 2,
x1 + x2 + λx3 = 2.
4. (20©) A ´n‘‚5˜mV þ ˜‡‚5C†, y²:
dim(A −1
(0)) + dim(A V ) = n,
ùpÎÒA −1
(0)L«A Ø, A V L«A Š•.
1 1 •
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