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Let P1 be the vector space consisting of all polynomial functions- Whi.docx

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28 jan. 2023

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Let P1 be the vector space consisting of all polynomial functions. Which
of the following are subspaces of P1? Justify you...

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Let P1 be the vector space consisting of all polynomial functions- Whi.docx

28 jan. 2023

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Let P1 be the vector space consisting of all polynomial functions. Which
of the following are subspaces of P1? Justify your answer in each case.
(a) The set of polynomials f(x) satisfying f(1) = 0.
(b) The set of polynomials f(x) satisfying f(0) = 1.
(c) The set of polynomials f(x) satisfying f(0) = f(1).
(d) The set of polynomials f(x) satisfying f(0)f(1) = 0.
(e) The set of polynomials of the form ax2 + bx + a, where a, b are any
real numbers.
Solution
(c) can be a vector space if f(0) = 0
(d) can be a vector space if f(0) = 0
.

Let P1 be the vector space consisting of all polynomial functions. Which
of the following are subspaces of P1? Justify your answer in each case.
(a) The set of polynomials f(x) satisfying f(1) = 0.
(b) The set of polynomials f(x) satisfying f(0) = 1.
(c) The set of polynomials f(x) satisfying f(0) = f(1).
(d) The set of polynomials f(x) satisfying f(0)f(1) = 0.
(e) The set of polynomials of the form ax2 + bx + a, where a, b are any
real numbers.
Solution
(c) can be a vector space if f(0) = 0
(d) can be a vector space if f(0) = 0
.

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Let P1 be the vector space consisting of all polynomial functions- Whi.docx

1. Let P1 be the vector space consisting of all polynomial functions. Which of the following are subspaces of P1? Justify your answer in each case. (a) The set of polynomials f(x) satisfying f(1) = 0. (b) The set of polynomials f(x) satisfying f(0) = 1. (c) The set of polynomials f(x) satisfying f(0) = f(1). (d) The set of polynomials f(x) satisfying f(0)f(1) = 0. (e) The set of polynomials of the form ax2 + bx + a, where a, b are any real numbers. Solution (c) can be a vector space if f(0) = 0 (d) can be a vector space if f(0) = 0