B Let V M 2 2 Let W Be The Collection Of All 2 2 Symmetric Matrices And U Be The

b)    Let V = M2×2. Let W be the collection of all 2 × 2 symmetric matrices and U be the set of all 2 × 2 skew-symmetric matrices.

i)      Assuming that W is a subspace of V , find a basis for W and thereby determine the dimension of W.

ii)    Assuming that U is a subspace of V , find a basis for U and hence determine its dimension. iii) Prove that if A ∈ V , then A = B +C with some B ∈ W and C ∈ U.

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