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# 這是一題有關calculus的問題 拜託幫幫我~

Suppose A is a 3 x 3 matrix such that A^4- 2A^3 + 5A^2 - 2I = 0. Show that A is invertible.

(Hint: think carefully about the defnition of invertibility of a matrix on page 264).

definition: if A is a square matrix and there exists a matrix C such that CA=I, then C is called

可以幫我求出來嗎? 拜託拜託>"<

Update:

then C is called an inverse of A, and A is said to be INVERTIBLE

### 2 Answers

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- linchLv 71 decade agoFavorite Answer
A^4- 2A^3 + 5A^2 - 2I = 0 ==> A^4- 2A^3 + 5A^2 = 2I

A ( A^3 - 2A^2 + 5A ) = 2I ==> A [ (1/2) A^3 - A^2 + (5/2) A ) = I

所以 (1/2) A^3 - A^2 + (5/2) A 是 A 的 Inverse

因此 A 是 invertible

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