Question

Please help and show all work. thank you!!!

20) a) Show that W={{#1: 3x=y=0} is a subspace of R? b) Show that W={{{]:*+244-32=2} is not subspace of R3

Answer 1

subspace let V(f) be a Vector space over field F. Then subset WCV is called sulespace of u if ta, BEF & UVEW, we can get, aut BV EW a let x,BER and u=(56,4), U=(0,7) EW clearly, 306-9, 30 and 304 70 since, 3.0-0 =0 (0,0) EW, i.e. W&O. Now, & UABU = 2(06, 9) + ß (02, G2) = (2+4+352, 79, +34) :"3(2x + Bxg)-(& J+ BY ) = 3434-49, +3832 - B92 = (3%, - y) + B (3762 - %) = 2(0)+ Blo)=0 aut BV EW hence w= 3x-1=0 RT is vector subspace of

0 +2.0*3.0= 0+2 hence, (0,0,0) & w w is not therefore clearly spac subs R3