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Determine whether S = { 1 - t , 2 t + 3 t 2 , t 2 - 2 t 3 , 2 +

Determine whether

S = {1 - t, 2 t + 3 t^{2}, t^{2} - 2 t^{3}, 2 + t^{3}}

is a basis for

P_{3} .

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