2. (5%) Let A, B, C, D be four n by n nonsingular matrices. What is the determinant of ?(A) det( A )det( B )det() (B) det( A )det( D )det(C) det( C )det(D - B) (D) det( C )-det(D -B) (E) none of the above

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

2. (5%) Let A, B, C, D be four n by n nonsingular matrices. What is the determinant of ?
(A) det( A )det( B )det()
(B) det( A )det( D )det
(C) det( C )det(D - B)
(D) det( C )-det(D -B)
(E) none of the above

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