13. (5%) Which of the functions T: R3→ R2 is NOT a linear transformation? (A) T(x,y,z)=(2x,y+z) (B) T(x,y,z)=(2x-1,z) (C) T(x,y,z) =(0,0) (D) T(x, y, z) = (x cosθ - ysinθ, ycos θ + z cosθ ) (E)T(x,y,z) =

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

13. (5%) Which of the functions T: R³→ R² is NOT a linear transformation?
(A) T(x,y,z)=(2x,y+z)
(B) T(x,y,z)=(2x-1,z)
(C) T(x,y,z) =(0,0)
(D) T(x, y, z) = (x cosθ - ysinθ, ycos θ + z cosθ )
(E)T(x,y,z) =

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