試題詳解

4. (5%) Which of the following is true?
(A) A linear transformation with codomain R^m is onto if and only if the rank of its standard matrix is m.
(B) A linear transformation is one-to-one if and only if its null space consists only of the zero vector.
(C) A linear transformation is onto if and only if the columns of its standard matrix form a generating set for its range.
(D) If the composition UT of two linear transformations T : Rn → R^m and U : R^P → R^q is defined, then m = p must be true and the composition UT is also a linear transformation.
(E) For every invertible linear transformation T, the function is also a linear transfor- mation.