Question

(1 point) Let T be a linear transformation. Which of the following statements could be used to describe 77 (Select all that apply.) A. T(0) = 0 B. The columns of T are linearly independent. c. T is not empty. D. The domain of Tis R'. E. T contains (ie.. ). E T is a 3 x 4 matrix. G. T is one-to-one.

Answer 1

Here T be a linar transformation, TOOD CA is true because if Tirow athen Zero veckor. v Contains T10-0 In V, Oto FO Since T is linear TO) in wi or Tlorf O) = [Tro) - T¢0)]= - T10) + Tio) - T10) in w. ETIO) + tro)] + Tro) Or 0 - 0 + 760) = 0 i T10-0 B is not true Tisnot empty (frue) The domain of T is sa T Contains o lies RO is not true. d To 5 ET) is true. e f T is matrix is not true a 3x4 T is one-to-one is not true که

For option B. Let T: P2 (R) – P2 (R) the defined Lini by T(4) FH $={1, 2, why be T(1) = x 0.1 front of Orur Standard basis T(a)=r = 0.1 ftill forget Tranan = 0.1 fl. nroiun (Line Then of P2 (R). 0 [I linearly are m Colums of of dependent, For option c Tis non emply because T Entains zero vector le BET. 65 For option Di T: P2 tr) Parere) by Tlf) = x. result (A). for option E by the ل 0 For option f - (tie kert= 503: 211 For option a t is one-for one