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設A的特徵值是a,則a^2-3a+2是A^2-3A+2E的特徵值. 由已知A^2-3A+2E = 0,而零矩陣的特徵值只能是零, 所以a^2-3a+2 = 0,即(a -1)(a - 2)= 0.所以a=1或a = 2. 即A的特徵值只能是1或2.
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