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 symmetric}
where R is the set of real numbers.
(Recall: A is symmetric if A^T = A)
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