Prove the subset is a subspace. A) Let F be a field and let V =...

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Prove the subset is a subspace. A) Let F be a field and let V = {(1, 2, 0, x4, 0) | x₁, x2, x4 € F}. Prove V is a subspace of F5 by explicitly showing the three parts of the Subspace Theorem are satisfied. B) Let V be a vector space over field F such that u₁, U2, U3, and u4 are in V. Let U = {a₁u₁ + a₂u2 + α3U3 + α₁U₁|α1, a2, a3, α₁ € F}. Prove that U is a subspace of V by explicitly showing the three parts of the Subspace Theorem are satisfied. Prove the subset is a subspace. A) Let F be a field and let V = {(1, 2, 0, x4, 0) | x₁, x2, x4 € F}. Prove V is a subspace of F5 by explicitly showing the three parts of the Subspace Theorem are satisfied. B) Let V be a vector space over field F such that u₁, U2, U3, and u4 are in V. Let U = {a₁u₁ + a₂u2 + α3U3 + α₁U₁|α1, a2, a3, α₁ € F}. Prove that U is a subspace of V by explicitly showing the three parts of the Subspace Theorem are satisfied.