Whichofthefollowingsetsareclosedunderscalarmultiplication?(i)ThesetofallvectorsinR2oftheform(a, b)wherea+4b=4.(ii)Thesetofall2 × 2matriceswhosetraceisequalto1.(iii)Thesetofallpolynomialsi
Whichofthefollowingsetsareclosedunderscalarmultiplication?
(i)ThesetofallvectorsinR2oftheform(a, b)wherea+4b=4
.(ii)Thesetofall2 × 2matriceswhosetraceisequalto1.
(iii)ThesetofallpolynomialsinP2oftheforma0+a1 x+a2 x2wheretheproducta0 a1 a2≤0.
(A)(i)only(B)(iii)only(C)(i)and(ii)only(D)(i)and(iii)only(E)noneofthem(F)(ii)and(iii)only(G)allofthem(H)(ii)only
Whichofthefollowingsetsareclosedunderaddition?
(i)ThesetofallvectorsinR2oftheform(a, b)whereb=a2.
(ii)Thesetofall3 × 3matricesthathavethevector[-232]Tasaneigenvector.
(iii)ThesetofallpolynomialsinP2oftheforma0+a1 x+a2 x2wherea0=a2.
(A)(ii)only(B)(i)and(ii)only(C)(ii)and(iii)only(D)(i)and(iii)only(E)(i)only(F)(iii)only(G)allofthem(H)noneofthem