複選題1.Let x and y be nonzero vectors in Rn, n ≥ 2. Suppose x and y are not orthogonal, i.e. xTy ≠ 0. Let A = xyT. Which of the following statements are true? (A) O is an eigenvalue of A. (B) xTy is an eigenvalue of A. (C) x is an eigenvector of A. (D) The number of linearly independent eigenvectors associated with eigenvalue 0 is n - 1. (E) A is diagonalizable.

複選題7. Let Pn denote the set of all polynomials of degree less than n. Which of the following statements are true? (A) Suppose V1, V2, V3 are linearly independent vectors in P3. Then V1, V2, V3 span P3. (B) If V1,V2, V3 are linearly dependent, then Span(v1, v2) must be equal to Span(v2, v3). (C) P2 is a subspace of P3. (D) Ifv1 + v2 + V3 equals the zero polynomial, then V1, V2, V3 must be linearly dependent. (E) If V1,V2, .., Vm span a vector space V, then V1, V2, ..., Vm must be linearly independent.

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