阿摩線上測驗
登入
首頁
>
中山◆電機◆工程數學乙
>
107年 - 107 國立中山大學_碩士班招生考試_電機系(乙組)：工程數學乙#113265
>
題組內容
1.(12%) Let
.
(b) (2%)Use the Fundamental Subspaces Theorem to show that N(A
T
A)
N(A).
其他申論題
②2 若賣方出口報價的計算式如下： (工廠價+運費)/(1-業務費率)/(1-利潤率)/(1-投保比率*保險費率)/(1-佣金率) 則該批貨物每件 CIP 報價為多少？ USD_____ 。(計算至小數點第三 位，四捨五入取二位) (2 分)
#483959
①1 關稅= NTD_____ 。 (元以下捨去) (2 分)
#483960
②2 營業稅= NTD_____ 。 (元以下捨去) (3 分)
#483961
(a) (2%) (i) What is the mathematic relationship of dimensions of two subspaces R(A) and N(A) for any A matrix considered here? (ii) What is the mathematic relationship described in the Fundamental Subspaces Theorem about matrix A ?
#483962
(c) (2%) (i) What is the condition on R(A) or N(A) that is equivalent to the existence of solution to Ax= b? (ii) What is the condition on R(A) or N(A) that is equivalent to the uniqueness of solution to Ax = b, if it is solvable?
#483964
(d) (2+4%) When the equation Ax = b is unsolvable, we may consider the so-called least squares problem to find a set of solutions, having the least squares error, from solving a normal equation. (i) Use the property and condition mentioned in (b)-(c) to explain why the normal equation is always solvable.
#483965
(ii) Suppose that rank(A) = k ＜ min(m, n) and let A = BC be a full rank decomposition of A . Use the known matrices B, C, and b to describe the unique projection vector p of b onto R(A) with the least∥b-p∥2.
#483966
(a) (1+2%) Let δ be a unit element of"t", the addition operation of V. (i) Write the equality condition about & as shown in the corresponding axiom. (ii) Let y be another unit element of "+". Show that δ=y.(須註明使用到的所有向量空間定義中的公設,否則不計分)
#483967
(b) (3%) Let X and Y be two subspaces of V. (i) Write the definition of XtY . (ii) Write the definition of X⊕Y . (ii) What is the mathematical relationship between dim (X⊕Y) and dim(X⊕Y)?
#483968
(c) (2%) Let 〈●，●) be an inner product defined on V. Show that the function defined satisfies the triangular inequality property.
#483969
.
N(A).
阿摩線上測驗
登入
阿摩線上測驗
登入
.N(A).