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轉學考-線性代數
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102年 - 102 淡江大學 轉學考 線性代數#53093
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5. Prove that |AB| = |A||B| for any nxn matrices A and B. (20 %)
其他申論題
(a) Prove that T is a linear transformation.
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(b) Find bases for ker J1 and imT , respectively.
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(c) Find Nullity{T).
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【已刪除】 4. LetA= (20%)Find |A| , adjA,A-l and adj(adjA).
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(a) Calculate P(A\B).
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(b) Are A and B independent events?
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(a) Determine the joint and marginal probability distributions of U and V.
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(b) Find out whether U and V are dependent or independent.
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3. (15%) Suppose we choose arbitrarily a point from the square with corners at (2,1), (3,1), (2,2)， and (3,2). The random variable X is the area of the triangle with its corners at (2,1), (3,1), and the chosen point. Compute E[X],
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(a) IF I = [a,β] (with a andβunknown, a ＜β. Find the maximum likelihood estimates (MLEs) for a and β.
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