(12%) Let V be a finite-dimensional vector space and T :V →V be linear. Suppose rank(T) = rank(T²). Prove that R(T) ∩N(T) = {0}.

(c) (3%) Compute rank(AtAAAt).

(d) (2%) Compute dim(N(Bt A)).

(10%) The nullities of the matrices BBT - λ/ for  λ= 0, 1,2,3, 4  are______,________,_________,_______ respectively. 

(13%) Given a vector space V over F. Define the dual space of V* of V as the set of all functions (also known as linear functionals) from V to F, i.e, V* {f|f : V →F}. It is obvious that V* is itself also a vector space with the addition + :V*'x V*→ V* and scalar multiplication * : F x V*→  V* defined as pointwise addition as well as pointwise scalar multiplication. Given any linear transformation T : V→  W. The transpose Tt is a linear transformation from W* to V* defined by Tt(f) = fT for any f W*. For every subset S of V, we define the annihilator Suppose V, W are both finite-dimensional vector spaces and T : V → W is linear. Prove that .N(Tt) = (R(T))0.

一、 試說明電子病歷的優勢，以及國內有關電子病歷的法令規定。

二、 試舉例說明如何建構一套醫療管理決策支援系統。

三、 當醫院系統開發已告一階段後，在正式系統上線前，為能讓上線執行一切 順利圓滿，都會擬出可能突發的狀況及處理的SOP，以備在各硬體裝置與 軟體系統執行運作中處理在演練中未發現的突發狀況。如果你身為系統開 發的專案主持人，請你列出需要檢核的清單與可能的突發狀況及處理的機 制與規畫。

(1) 請說明一下微服務系統開發與傳統系統開發的相異處。

(2) 請說明微服務開發需要的條件。

(1) 請分析各類使用者可能會有那些資訊化的需求。