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無年度 - 主題課程_對角化：對角化#107843
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題組內容
107中與資工
Let A=
(a) (3%) Find the eigenvalues of A. ul
其他申論題
Three events: A1, A2 and B are given. We know that A1 and A2 are disjointed events. P(A1)>0 and P(A2)>0. Let P(B|A1)= P(B|A2)=0.2. Please find P(B|A1UA2).
#462058
(b) (6%) Is A diagonalizable? Justify your answer.
#462063
107台大資工 (10%) Your answer will be considered correct only if all the true statements are selected. Let A be an nxn matrix. (a) If x1 and x2are the cigenvectors of A, then x1 + x2 is also an eigenvector of A. (b) If AT = -A, then A is singular. (c) If A2 = A. (A+1)n = 1 + (2n+1)A. (d) If A = AT, then A is diagonalizable.(e) If A = and B and D are invertible,then.
#462064
110交大資訊聯招 b.(10 points) Given a sequence 7, -6, 20, -24, 64, -96,... comes from for k ≥ 0, with G0 = 7, G1 = -6 and G2 = 20. Please find the number .
#462065
(a) (4%) What are the values of G4 and G5?
#462066
(b) (5%) Give a matrix A such that
#462067
(c) (5%) Find an explicit formula for Gk.
#462068
(d) (6 %) What is the limit of Gk as k →∞?
#462069
109北科大電子_工數 ㆍ(12%) Find an explicit formula for the sequences defined recursively by
#462070
105交大資訊聯招 (6points) Three persons, TC, CC, and YJ, have their own gold. They always divide their own two equal parts and donate to others every day. IC, for example, has 12-kilograms gold today and donate 6 kilograms to Cc and the other 6 kilograms to Y.. If TC has 6 kilograms, CC has 1 kilogram, and YJ has 2 kilograms at first, how many kilograms of gold do CC and YJ have after 365 days?
#462071
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