Let P₂ denote the vector space of polynomials of degree up to 2. Which of the following subsets of P₂ are subspaces of P₂? A. {p(t) | p(−t) = p(t) for all t} B. {p(t) | p(5)=0} c. {p(t) | p(2) = 1} ] D. {p(t) | p′ (1) = p(0)}

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A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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A: a=1b=-2c=5Explanation:

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: a=1, b=-2, c=5Explanation:Step 1: Step 2: Step 3: Step 4:

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A: We can just multiply h and k and integrate  Then after simplifying we are getting answer

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A: is defined by .We have to find a vector  whose image under  is  where .

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A: Step 1:Step 2: Step 3: Step 4:

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