The set of all polynomials of degree 6 under the standard addition and scalar multiplication operations is not a vector space because * We can find two polynomials P(x) and Q(x) for which P(x) Q(x)#Q(x)·P(x) We can find a polynomial P(x) for which 1 P(x)=P(x) It is not closed under addition. We can find a polynomial P(x) such that (c+d)P(x)#cP(x)+dP(x). [1 2 31 Let A = |1 3 9. Then the adjoint of A is given by: li 5 7

Q: (3) For each of the following sets, determine whether it is linearly independent or dependent. (a)…

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

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Q: An operator whose minimal polynomial is different from its characteristic polynomial

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Q: Use the inner product (p, q) = abo + a,b, + a,b, to find (p, q), ||p ||, ||9||, and d(p, q) for the…

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Q: Find a basis {p(x), g(x)} for the vector space {f(x) = P₂[x] | f'(3) = f(1)} where P₂ [x] is the…

A: Here we have to find the p(x) and q(x) that are basis of given vector space.

Q: Find a basis {p(x), q(x)} for the vector space {f(x) = P₂[x] | ƒ'(-3) = f(1)} where P₂[x] is the…

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Q: Use the inner product (p, q) = aobo + a₁b₁ + a₂b₂ to find (p, q), ||pl|, |la||, and d(p, q) for the…

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Q: Use the inner product (p, q) = abo + a,b, + a,b, to find (p, q), ||p ||, ||9||, and d(p, q) for the…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: 2d

A: Definition of P2​(R): Space of polynomials of degree at most 2 with real coefficients.Introduction…

Q: factor x as a product of three linear polynomials in Z/30Z[x] by using Chinese remainder theorem

A: Ans- To factor x as a product of three linear polynomials in Z/30Z[x], we first need to factor 30…

Q: 7. Prove that M2x2(C) is a complex vector space under the usual addition and scalar multiplication…

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