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• 4. (12 points) Let . Show that if rank(AB) = m,then rank(BA) =m.
• 2. Ho: The coefficient of BM is zero. Ha: The coefficient of BM is not zero. You test H0 using a t-t
• 【題組】(b) (4 %) Please show that the average energyis
• 【題組】(e) (3%) Let A be an m x n matrix. If the number of pivot numbers of A is less than m, then Ax =
• 3. IfX1，X2, .... Xn are mutually independent normal random variables, with their means all equal to
• 2.Which of the following statements are correct?(A) The dynamic power dissipation of CMOS is proport
• 2. (10%) Let W1, W2,... , be subspaces of  such that  is a subset of  is the orthogonal complement o
• 5. Let T: V→ V be a linear operator on a finite-dimensional F-vector space V.【題組】(a) (6 points) Stat
• 【題組】(b) (6 points) Give an explicit example of T that has no eigenvectors.
• 【題組】(c) (8 points) Prove that T has an eigenvector if F = C.
• 29 關於雙載子電晶體 （BJT）的小信號模型，下列敘述何者錯誤？ (A)在特定 β 的條件下， 與偏壓電流成正比 (B)在特定 β 的條件下， 與偏壓電流成正比 (C)在特定元件大小的條件下，
• 61. 有關「門」的 CNS 建築圖例及名稱，下列何者正確？ (A) ：雙向門 (B)：折疊門 (C) ：旋轉門 (D) ：上拉門 。
• 6. (10 points) Let is an invertible matrixsuch that AQ is diagonal, then each column vector of Q is
• 3. Given the IEEE-754 single precision floating-point operand format as follows, (A) The decimal num
• 4. Y is distributed , and K is distributed . Suppose Probability(Y S 16) = 0.90. Please calculatePro
• 3.(a) (8%) Find the eignevalues and eigenvectors for
• 【題組】(c) (14%) Express the Boltzmann distribution in terms of speed and show that the most probable s
• 2.如圖,圓O1、O2相交C、D兩點,已知圓O1半徑13,圓O2半徑20,=,其外公切線交兩於A、B兩點,連接=?(10分)(註:132=169，142=196，202=400，212=441)
• 7. (12 points) Let T:Rn→ Rn be a linear operator. Show that if T preserves theEuclidean distance bet
• 34 患者必須進行一系列的注射。任何一次注射出現不良反應的機率為 0.1，並且在兩次不良反應後必須停止注射。如果這些注射是獨立的，注射暫停時正好有 5 個注射是沒有不良反應的機率為何？ (A) (B
• (b) (3%) How can you tell whether a matrix is invertible from its eigenvalues?
• (c) (3%) How can you tell whether two matrices are similar from their eigenvalues?
• 4. (a) (8%) For the following matrix, find the bases for its row space and nullspace.
• 8. (12 points) Let be a real symmetric matrix. Show that there existsa real symmetric matrix B such
• 5. A random draw (with replacement) of 1000 balls from a pool of several million balls is conducted.