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Determine the dimension of w

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Reference no: EM132015769

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.

Reference no: EM132015769

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