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Solve 4 questions of quiz. each of them gives 0.25 point 1. Show that the following...

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Basic Math

Solve 4 questions of quiz. each of them gives 0.25 point

1. Show that the following sets of elements in R3form subspaces. (a). The set of all (x, y, z) such that x ? 2y + z= 0. (b). The set of all (x, y, z) such that x = 3z and y = z.

2. (a). Let U = {(x, y) ? R2 : 0 ? x ? 1 and 0 ? y ?1} and W = {(x, y) ? R2 : x 2 + y 2 ? 1}. Are these setssubspaces of R^2? (b). Find the sum U + W.

3. If U and W are subspaces of a vector space V, show that U + Wis a subspace

4.Show that functions f(t) = t and g(t) = 1/t defined for t >0 are linearly independent.

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