14. (5%) Let A, B be square matrices. Suppose the determinants of A2B3 and A3B2 are det(A2B3) = 1125 and det(A3B2) = -675, respectively. What are det(2A) and det? (A) (B) (C) (D)(E)

4. (5%) Let A be an m by n matrix. Which statement is TRUE? (A) The null space of A is a subspace of the column space of AT (B) The dimension of the null space of A plus the dimension of the row space of A is (C) The null space of AT equals column space of A (D) The column space of A is orthogonal to the row space of AT (E) The direct sum of the row space of A and the null space of AT is Rm

14. (5%) Let A, B be square matrices. Suppose the determinants of A²B³ and A³B² are det(A²B³) = 1125 and det(A³B²) = -675, respectively. What are det(2A) and det?
(A)
(B)
(C)
(D)
(E)

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