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Determine which of the following sets is a subspace of Pn for an appropriate value of n.A: All polynomials of the form p(t) = a + bt2, where a and b are inB: All polynomials of degree exactly 4, with real coefficientsC: All polynomials of degree at most 4, with positive coefficients

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All polynomials of the form p(t) = a + bt2, where a and b are in sets is a subspace of Pn for an appropriate

Step-by-step explanation:

Consider the following subsets of Pn given by

The 0 vector of V is in W.

- Given v,w in W then v+w is in W.

- Given v in W and a a real number, then av is in W.

So, for us to check if the three subsets are a subset of Pn, we must check the three criteria.

First property:

Hence the first criteria is not met. Then, W2 is not a subspace of Pn.

For W1 and W3, note that if a= 0, then we have p(t) =0, so the zero polynomial is in W1 and W3.

W1 and W3 are subspaces of Pn for n= 2

and W2 is not a subspace of Pn.  

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