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  3. let v = r4 and let u = hu1, u2i, where u1 =? ? ?..

Let V = R4 and let U = hu1, u2i, where u1 =? ? ?...

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Advance Math

Let V = R4 and let U = hu1, u2i, where u1 =? ? ? ? 1 2 0 ?3 ? ?? ?, u2 = ? ? ? ? 1 ?1 1 0 ? ? ? ?. 1. Determine dimU and dimV/U.2. Let v1 =? ? ? ? 1 0 0 ?3 ? ? ? ?, v2 = ? ? ? ? 1 2 0 0 ? ? ? ?,v3 = ? ? ? ? 1 3 ?1 ?6 ? ? ? ?, v4 = ? ? ? ? ?2 2 0 9 ? ? ? ?. Forany two of the vectors v1,...,v4, determine whether they are in thesame coset of U in V or not. 3. Find a basis of V that contains abasis of U. Hence, determine a basis of V/U. 4. Find two (distinct)elements of the coset e1 + U.

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