Let V be the vector space P3[x] of polynomials in x with degree less than 3 and W be the subspace W = span{3 - 2x - 3x^2, -(6 + 5x + 5x^2)}. a. Find a nonzero polynomial p(x) in W. p(x) = b. Find a polynomial q(x) in V but not in W. q(x) =
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First, we need to find a nonzero polynomial p(x) in W. Since W is the span of the given polynomials, we can write p(x) as a linear combination of these polynomials: p(x) = a(3 + 2x + 3x^2) + b(6 + 5x + 5x^2) where a and b are scalar constants. Show more…
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