Please find the eigenvalues and eigenvectors of given

說明：請將以下短文中劃底線處之中文句子譯成正確、通順、達意的英文(一)中譯英(8 分)① 近年來，許多發展中國家經歷了社會與經濟的巨大危機。 社會經濟困境改變了能 源方面的投資，並因移動限制嚴重影響產業發展。大多數投資活動因而面臨中斷。 ② 雖然面對政治緊張所帶來的紛亂，有些公司年營收仍創歷史新高。

(二)英譯中(8 分)        Playing sports has a major influence on a person’s health. It brings good qualities to one’s life. ③ Doing exercise properly and correctly and achieving a fitness goal can strengthen sportsmen’s core muscles and boost their athletic performance. However, sporting activities have both good and disruptive effects on one’s health. ④Positive effects from workouts are accomplished primarily through physical activities, but negative impacts of excessive movements include increased injuries and extreme fatigue.

(1) 對圖表的描述與分析：分別描述 iOS 及 Android 系統在此期間市占率的趨勢變化； 並比較兩大系統的市占率差異。

(2) 在購買智慧型手機時，作業系統會是你考量的因素嗎？為什麼？

Let and f(s) = s4 - 13s3 + 17s2 - 13s + 87. Please find f(A).

Let .Please find f(A), where f(t)=t4-3t3-6t2+7t+2.

If A is an nxn matrix, derive the characteristic polynomial of A. 

(a) Find the eigenvalues of A

(b) Find the determinant of A

(c) Based on (a), state whether A is invertible or not