複選題

,Let A = and define a transformation T : R² → R³ by T(x) = Ax. Which 1-1 of the following statements is/are true?
(A) The image of x = under T is .
(B) There is exactly one x whose image under T is. 
(C)The vector b is in the range of T if b is the image of some x in R².
(D) The vector b is in the range of T if the system Ax = b is inconsistent.
(E) The vector is not in the range of T. 

32.1, -3 are in the  β-matrix. (A) True. (B) False.

33. -2, -4 are in the  β-matrix. (A) True. (B) False.

34.-6, -7 are in the β-matrix. (A) True. (B) False.

35. 8, -9 are in the  β-matrix. (A) True. (B) False.

複選題Consider the linear equation Ax = b with A . Which of the following statements are true? (A) Ifrank( A ) = m, then there exists at least one solution. (B) If rank( A ) = n, then there exists exactly one solution. (C) Ifrank( A ) = n, then the column vectors of A are lincarly indcpendent. (D) Ifn ＞ m, then there exists at least one solution. (E) Ifm ＞ n, then there exists at most one solution.

複選題ㆍLet A be an m✕  n real-valued matrix of rank r. and b be an m✕ 1 real-valued vector. Which of the following statement is/are true? (A). The equation Ax = b has non-trivial solutions if n ＞ r ＞ 1 and b is all-zero. (B). The equation Ax = b has solutions if b belongs to the column space of A. (C). The equation Ax = b has only one solution when r = m. (D). The dimension of the nullspace of A is O if the dimension of the row space of A is r. (E). None of the above is true.

複選題十三. Let X be a continuous random variable with probability density function Sx. In addition, fx(x) = , (0, 1]. Furthermore, P(X ＞ 1) = P(X ≤ 0) = 0. Moreover,f jx(t) ＜∞ , Vt E (-∞,∞). Which of the following statements is/are true? (A)(B)(C) (D) (E)

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