Let V = R4 and let U = hu1, u2i, where u1 =   ...

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    . For any two of the vectors v1,...,v4, determine whether they are in the same coset of U in V or not. 3. Find a basis of V that contains a basis of U. Hence, determine a basis of V/U. 4. Find two (distinct) elements of the coset e1 + U.

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Colby Messinger answered 1 year ago

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