Let U , V be subspaces of of vector W Use the examples U={ (x,0)l x in R } and V={ (0,y) l y in R }, W=R^2 to show that U u V isgenerally not a subspace.
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Use the Chain Rule to find the indicated partial derivatives. z = x^3 + xy^2, x = uv^2 + w^3, y = u + v*e^w [(partial z)/(partial u), (partial z)/(partial v), (partial z)/(partial w)] when u = 2, v = 1, w = 0 [(partial z)/(partial u)] = ? [(partial z)/(partial v)] = ? [(partial z)/(partial w)] =?