Question

Check whether the set 

S = {(al, a2, ..., an) E Rn I a1= 1 + a2} 

is a subspace of Rn or not. 

Answer 1

we have to check if the set is subspace or not

solution:

according to the question given

$S=(a_1,a_2,.....a_n)$ ,is a sub set of $R_n$ ,

according to the definition of subspace the set $(0,0,0,0,0......nth)$ have to belong to S,

As it is given that $a_1=1+a_2$ then it is clear that all the n elements can not be 0 at a time so

(0,0,0,0,0,......) can not belong to S.

Hence the set S is not a subspace.