please need an accurate answer 7 The following regions are n

please need an accurate answer

7 The following regions are not subspaces of R2. For each example give pairs of a vectors or a pair of a vector and a real number that demonstrates this

Solution

(1) Consider the pair of vectors (1,0) and (0,1).

Their sum is (1,1) which does not belong to the subset.

So it is not a subspace.

We may also consider the vector (1,0) and the scalar 4.

4(1,0) =(4,0) does not belong to the subset.

(2) Again , the same set of vectors suffice to show that this is not a subspace.

(1,0) and (0,1) belong to the subset but not their sum (1,1).

(3) Consider the vectors (2,-3) and (-2,2) belong to the subset.

But their sum (0,-1) does not belong to the subset.

So it is not a subspace.