試題詳解

Which of the following is true?
(A) A linear transformation with codomain 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 : and U : 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.