3. Let ē = (1,0,0)", 2 = (0, 1,0)", s = (0,0, 1)" be the standard basis of R*. Consider a linear map T : R* → R* satisfying T (r, y, 2)") = (0,0,0)" whenever 2x – y+ z = 0. (a) Show that T (. 0, –...

• pls help for part D)

Extracted text: 3. Let ē = (1,0,0)", 2 = (0, 1,0)", s = (0,0, 1)" be the standard basis of R*. Consider a linear map T : R* → R* satisfying T (r, y, 2)") = (0,0,0)" whenever 2x – y+ z = 0. (a) Show that T (. 0, – 1)") = (0,0,0)" and T ((0, 1, 1)") = (0,0,0)". %3D %3D (b) Justify whether T is an isomorphism using result from (a). (c) Given T(ēs) = (1,2, 3)T. Find T (č) and T () by using result from (a). (d) Use your results of T(ei), T(ē2), T(ēs) to determine the image of an arbitrary vector (r, y, 2)T E R under T.