Linear Algebra Consider the following subset W of the given vector spaces V . (i) Find two nonzero (non-trivial) elements in W and justify why they belong to W. (ii) Determine whether W is a subspace...

Linear Algebra

Consider the following subset W of the given vector spaces V .

(i) Find two nonzero (non-trivial) elements in W and justify why they belong to W.

(ii) Determine whether W is a subspace of V . Give proof if it is, or a counter example if it is not.

V = M_(n×n)(R), W = {A ∈ M_(n×n)(R) | A is invertible}

where R is the set of real number.