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Let V= $R^3$ show that W is a subspace of $R^3$ where W={(a,b,c)=a+b+c=0},that is W consist of all vectors where the sum of their component is zero.
1 Answer
written 5.1 years ago by | • modified 5.0 years ago |
O=(0,0,0) belongs t0 W
Since 0+0+0=0 a'+b'+c' =0,
Suppose, u = (a, b, c) and v = (a', b', c')
Than a+b+c=0 and a'+b'+c'=0,
Therefore any scalars K and K' we have ,
Ku + k'v = K(a, b, c) +K'(a', b', c')
k(a,b,c)+K'(a',b',c') = k(a,b,c)+k'(a',b',c')
(ka+k'a)+(kb+k'b') +(kc+k'c') = (ka+k'a')+(kb+k'b')+(kc+k'c')
=0
Thus Ku +k'v belongs to W
$\therefore$ W is subspace of v.