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110年 - 110 國立中山大學_碩士暨碩士專班招生考試_海下所:工程數學#104424
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3.Let
. Find a symmetric matrix B and a skew-symmetric matrix C, such that B+C=4. 1 0] (5%)
其他申論題
5. (20%) Let x = (X1, X2, X3)' have a trivariate normal distribution with means 6, 4, and 2 and variance 16, 25, and 64, and with cou(X1, X2) = 6 and coc(X1,X3) = 4 and cou(X2,X3)=5. Let Y1=2X1+3X2+ X3 +2 and Y2 =4X1+ X3 +3. What is the joint distribution of y = (Y1, Y2)'?
#442070
1. Evaluatefor any a > 0. (5%)
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(1) Let u1 = <3, 1>, u2= <1, 1>. Transform them into an orthonormal basis. (5%)
#442072
(2) Let u1 = <1, 1, 1>, u2 = <1, 2, 2>, u3 = <1, 1, 0> . Transform them into an orthonormal basis. (5%)
#442073
4.Solve +y=x, y(0)=3.(10%)
#442075
(1) Find L{sin(2t)}. (5%) (Write down the detailed process)
#442076
(2) Solve +3y= 13sin(2t), y(0)=6.(15%)
#442077
6.Please write down the Bessel's differential equation. (7%)
#442078
7. Find y when y"x2 + (x2 -81)y = -xy'.(10%)
#442079
8.Find the eigenfunction of the following equation: y"+ ky =0, y(0)-y(L)-0.(15%)
#442080