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101年 - 101 國立交通大學_碩士班考試入學試題_電機工程學系:微分方程與線性代數#105738
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題組內容
1. (15%) Please determine whether the following statements are TRUE or FALSE. No explanations are needed.
(e) (3%) Let A be an m x n matrix. If the number of pivot numbers of A is less than m, then Ax = b has more than one solution.
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3.(a) (8%) Find the eignevalues and eigenvectors for
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(b) (3%) How can you tell whether a matrix is invertible from its eigenvalues?
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(c) (3%) How can you tell whether two matrices are similar from their eigenvalues?
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4. (a) (8%) For the following matrix, find the bases for its row space and nullspace.
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(b) (3%) In R3, is xy plane orthogonal to xz plane ? Explain it.
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(a)
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(b)
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6. (10%) Consider the following second order ordinary differential equation:Determine the solution y(x) satisfying the conditions y"(0) = 1 and y""(0) = 0.
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(a) (5%) Find the Laplace transform of f(t) and determine its region of convergence.
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(b) (10%) Solve the above ordinary differential equation (1) for y(t)
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相關試卷
101年 - 101 國立交通大學_碩士班考試入學試題_電機工程學系:微分方程與線性代數#105738
101年 · #105738