(7%) A=[[1,2,0,1],[1,1,1,0]],S={[[-3],[1],[2],[1]],[[0],[-1],[1],[2]],[[-3],[-1],[4],[5]]}. Which of the following statements are true?
(A) Let T_(A) be the matrix transformation induced by the matrix A.T_(A) is one-to-one.
(B) Let T_(A) be the matrix transformation induced by the matrix A.T_(A) is onto.
(C) The dimension of the range of T_(A^(T))=2.
(D) Nu llA=SpanS.
(E) Let B_(1) be any basis for the range of T_(A^(T)) and B_(2) be any basis for Span S. Then B_(1)cup B_(2)
constitutes a basis for R^(4).
3. (7%)
-3] 0 [-3] 1 -1 12 Which of the following statements are
2 0 1 1
S
true?
(A) Let Ta be the matrix transformation induced by the matrix A. T. is one-to-one. (B) Let Ta be the matrix transformation induced by the matrix A. Ta is onto.
(C) The dimension of the range of Tar = 2.
(D) Null A = Span S.
(E) Let B, be any basis for the range of Tar and B, be any basis for Span S. Then B, U B,
constitutes a basis for R4.