試題詳解

5. Let V be the vector space of all A ∈ , with the operations of matrix addition and
multiplication of a matrix by a real scalar. Let T be a linear transformation from V to
Y, and (B₁,B₂,... ,] be a basis for V. Suppose U is a linear transformation from D to
given by U(c₁B₁ + c₂B₂ +.... +) = Which of the following
statements is/are true?
(A) Let(A₁, A₂,... ,] be linearly independent over R. The set ｛U(A₁),U(A₂),... ,｝
can be linearly dependent over .
(B) Suppose the dimension of the range space of T is k: over IR. Then ｛T(B₁),T(B₂),... ,｝
are linearly independent over .
(C) n=m.
(D) Let  c = U(B₁) and  a = U(T(B₁), then

(E) None of the above is true.