Question

Define the linear transformation T by T(x) - Ax. Find ker(T), nullity(T), range(T), and rank(T). 7-5 1 -1 (a) ker(T) (0.0) 0 (c) range() O R3 (6s, 6t, s - t): s, t are any real number) O (s, t, s-6): s, t are any real number) O ((s, t, o): s, t are any real number) (d) rank(T) 2 Need Help? Read It Talk to a Tutor Suomit Answer Save gssPracice Another Version Practice Another Version

Answer 1

From the 2nd ond 3rd equation ue7cl nyso, -o and alooit Ker (T): Ker (T) and ince nulty (T)-dimension of , tRn, Rege (T) e) rSince IU,o), (GN3 is a basis of the doroun sPaee is tho linar span of气he veeton T·U, o) and T(0, ) . Now T(I,o) = (7.1-S. 0, 1+0,1-0) (7,1,1) aud T(0.1): (7.0-s.), 0+,0-1) = (-5,1,-) G, t.) span ơ} tho veetas the linear auol (,1) Hence whore x, y are rend numbers, we put χ= 5tts ,y= Ram Cas, 6t, s-t): s, t ave any real num ber ) ら戉/>etd-linearly independen vee-fens , we get ie mn K (T) = 2