HW6.4. Determine if each of the following sets is a subspace of P₂. If the set is a subspace, prove your answer, and if it is not, explain why. a. The set W₁ of all polynomials of degree equal to 2; b. The set W₂ of all polynomials of the form t² +b; c. The set W3 of all polynomials of the form ať² +b.

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HW6.4. Determine if each of the following sets is a subspace of P₂. If the set is a subspace,
prove your answer, and if it is not, explain why.
a. The set W₁ of all polynomials of degree equal to 2;
b. The set W₂ of all polynomials of the form ť² +b;
2
c. The set W3 of all polynomials of the form at² +b.
Transcribed Image Text:HW6.4. Determine if each of the following sets is a subspace of P₂. If the set is a subspace, prove your answer, and if it is not, explain why. a. The set W₁ of all polynomials of degree equal to 2; b. The set W₂ of all polynomials of the form ť² +b; 2 c. The set W3 of all polynomials of the form at² +b.
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