Question

20. Consider the transformation from R →Rdefined by T(x, y, z) = (x + y, z). a. Under this transformation, find the image of the ordered pair (1, -3, 2). b. Is the transformation linear? Show your work! [5 marks]

Answer 1

Solution; (2.) The tram formatiom Te,8,2) = f2+d,7) %3D (1 -3, 2) Them T,-3,?) T(L-3,2) - - (-2,2) (-2, 2) ia he image of cL-32) Um aeo this toans formaßiam. IfTilimearr them TCa+P) = c T (d) + T(P) for all d, ßE R? Omd cER. d= (2,, bi,2W, ß= m,2,22) € 8°anel cER. - (C 4, CY,C 21) + (ao.2, 22) ca1+ 22, Cy + e Y2g CH + 22 ) Tc&t f)= T cea+12, cyI +82, CZ++Z2) (eM +22 + c Y+ Y2, C21+ 22)

(e faresi), ca1) +( s-32,' - c (2, 21) + (2+s, 22) T(P) ,22) ( 12+ 92, Hemce Tea+P) -C7(4) +7(B ) for al a, pE R amd CER. Hemce T i29 linears tooms foomatiom.