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.

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written 6.7 years ago by

teamques10 ★ 70k

• modified 5.7 years ago

engineering mathematics

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written 6.7 years ago by

teamques10 ★ 70k

• modified 6.7 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')

Thus Ku +k'v belongs to W

$\therefore$ W is subspace of v.

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