1. Let
be the reduced row echelon form of a matrix A = . Which of the
following statements is/are true?
(A) is the 4 x 1 zero vector.
(B) The three column vectors , are linearly independent.
(C) The column space of R is the same as the column space of A.
(D) Let B = be a submatrix of A. The reduced row echelon form of B is
not always a submatrix of R.

(E) None of the above is true.
R=

27. 如圖 17 所示電路，若 OPA 為理想，當頻率分別為 15.9Hz 及 1.59kHz 時，則以下電壓增益何者為最佳答案？ (A) 0dB, 0dB (B) 0dB, 20dB (C) 20dB, 0dB (D) 20dB, 20dB

28. 二極體電路如下圖 18(a)，兩二極體均具有如下圖 18(b) 之順向特性曲線，試問開關 S 打開及關閉，輸出電壓變化? (A) 0.25V (B) 0.2V (C) 0.15V (D) 0.1V

29. 下列有關稽納二極體之敘述， 何者錯誤 ？(A)累增崩潰時其稽納電壓為正溫度係數 (B)稽納崩潰時其稽納電壓為負溫度係數 (C)累增崩潰電壓往往是大於6V (D)稽納崩潰是由於熱效應所引發。

30. 有一電壓調整器如下圖 19 所示，其中稽納二極體為 4.7V 且最小工作電流為 12mA，若負載的變化範圍由 15mA~100mA，現若提供輸入直流電源 15V 時，試求該電路最佳 R₁ 電阻值至少為若干？ (A) 91Ω (B) 81Ω (C) 71Ω (D) 61Ω

2. Continue from Question -. Which of the following statements is/are true?(A) The nonzero rows of R form a basis for col.(B) Let C be the reduced row echelon form of . Then is the identity matrix.(C) Let E be a 3 x 5 matrix and[10110]D = 01110100001be the reduced row echelon of E. We can obtain the intersection of the right nullspace of A and the right null space of E from R and D without knowing A and E.(D) Let Q be a 5 x 5 matrix and rank(Q) = 3. Then rank(AQ) = 3.(E) None of the above is true.

3.Let U and V be subspaces of and T be a linear transformation from to . Whichof the following sets is/are subspace(s) of ?(A) (B)(C)(D) (E) None of the above is true.

複選題4.Let A, B, and C be n x n matrices for some positive integer n. Which of the followingstatements is/are true?(A) det( A ) = 0 implies det(R) == 0, where R is the reduced row echelon form of A.(B) If AB = CA - , then B = C.(C) If det(AB) 7 0, then A is invertible.(D) rank(AB)=rank(BA).(E) None of the above is true.

5. Let V be the vector space of all A ∈ , with the operations of matrix addition andmultiplication of a matrix by a real scalar. Let T be a linear transformation from V toY, and (B1,B2,... ,] be a basis for V. Suppose U is a linear transformation from D to given by U(c1B1 + c2B2 +.... +) = Which of the followingstatements is/are true?(A) Let(A1, A2,... ,] be linearly independent over R. The set ｛U(A1),U(A2),... ,｝can be linearly dependent over .(B) Suppose the dimension of the range space of T is k: over IR. Then ｛T(B1),T(B2),... ,｝are linearly independent over .(C) n=m.(D) Let  c = U(B1) and  a = U(T(B1), then (E) None of the above is true.

6. For the matrixwhich of the following statements is/are true?(A) rank( A ) = 3.(B) The sum of eigenvalues of A is 6.(C) A is similar to B =(D) The system of linear equations A x = has a solution.(E) None of the above is true.

複選題7. For a non-zero matrix A ∈ , deine(1)the maximum Frobenius norm ||A  x llover all unit-norm vectors  x . Which of the followingstatements is/are true?(A) σ2 is the maximal eigenvalue of .(B) If x0 is an optimal solution to equation (1), i.e, llAx0ll = σ, then there exists a vectorx1 such that Ax1 = 0  and ≠0.(C) Assune m = n and A is nonsingular. Then = .(D) Assume m = n. Then t A is singular only if σ ≥ 1.(E) None of the above is true.