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研究所、轉學考(插大)-基礎數學
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112年 - 112 國立臺北大學_碩士班入學考試_統計學系﹕基礎數學#130312
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題組內容
2.
(a) Write down the characteristic polynomial of A and use it to find the eigenvalues.
其他申論題
(a)
#552126
4. Where μ and , i = 1,2,...,n are known values. Find the value of σ at which L(σ) has its maximum. (Skip any derivative test)
#552127
(a) Please write down the (i,j)-entry of the product BCA in terms of Sigma notations (i.e. Σ).
#552128
(b) Please prove that .
#552129
(b) Find the eigenspaces of A.
#552131
(c) Orthogonally diagonalize the matrix A. (You need to find out an orthogonal matrix P and a diagonal matrix D such that PᵀAP = D.)
#552132
3. Let T: V → W be a linear transformation and B = be a spanning set for V. Please show that T(B) = spans the range of T.
#552133
(a) Prove that xᵀAx = 0 for all x ∈ .
#552134
(b) Prove that I + A is invertible.
#552135
(b) (10%) The integral in (a) can be approximated by integrating the linear approximation of the integrand, i.e. let f(x) = (1+x) / √(1-x²) ≈ f(0) + f'(0) x Approximate ∫-1^0 f(x) dx by evaluating ∫-1^0 (f(0) + f'(0) x) dx
#552136
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