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109年 - 109 國立臺灣大學_碩士班招生考試_資訊工程學研究所:數學(含線性代數和離散數學)#105828
> 申論題
6. (10%) Prove the following inequality:
where 2≤n.
相關申論題
1.(5%) Consider x1+x2+⋯+xn=r, where a≤xi≤sb for I ≤i≤n. What is the generating function for the eger solutions to the above equation (where the desired count appe coefficient of x', where r=0,1,...)?
#450911
2. (5%) What is the number of functions from {1,2....n}mto{1,2...，i}j?
#450912
3. (10%) Consider x1+x2+⋯+xn<r, where xi≥0 for 1 ≤i≤n. What is its number of nonnegative integer when n=4 and r=8?
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4. (10%) Derive the solution for an that satisfies the recurrence equation
#450914
5. (10%) The generating function in partial fraction decomposition for the above recurrence equation is___________ .(Note that expressions like are not partial fraction decompositions.)
#450915
7. (10%) If the polynomial function f(x) = ax4 + bx3+ cx2 + dx+ e satisfies, then a,6, c, d,e are______，_______ ，_________，________，_________， respectively.
#450917
8.(10%) The nullities of the matrices BBT - λ I for λ = 0,1,2,3,4 are______，_______ ，_________，________，_________， respectively.
#450918
9.(10%) Let Let The numbers of elements -2, -1,0, 1, 2 in a matrix B with are______，_______ ，_________，________，_________， respectively.
#450919
10. (10%) Ifthen the numbers of elements -2, -1 0, 1, 2 in a matrix B withare______，_______ ，_________，________，_________， respectively.
#450920
11. (10%) The numbers of elements 0, 1, 2, 3, 4 in a Jordan normal form of the matrixare______，_______ ，_________，________，_________， respectively.
#450921
相關試卷
110年 - 110 國立臺灣大學_碩士班招生考試_資訊工程學研究所:數學(含線性代數、離散數學)#102151
110年 · #102151
109年 - 109 國立臺灣大學_碩士班招生考試_資訊工程學研究所:數學(含線性代數和離散數學)#105828
109年 · #105828
108年 - 108 國立臺灣大學_碩士班招生考試_資訊工程學研究所:數學(含線性代數和離散數學)#106050
108年 · #106050
where 2≤n.
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where 2≤n.