3. Let P2 be the vector space of all real polynomials of degree at most 2. Let P1, P2, P3 Є P2 be given by p₁(x) = 3x, p2(x) = 2x + x², and p3(x) = B+ax². a) (4 marks) Find the condition on a, ß ER that ensures that {P1, P2, P3} is a basis for P2. (You are free to assume that the polynomials 1, x and x² are linearly independent.) b) (2 marks) In the case ẞ = 1, write the polynomial p(x) = 1 - x - x² combination of P1, P2 and P3. as a linear
3. Let P2 be the vector space of all real polynomials of degree at most 2. Let P1, P2, P3 Є P2 be given by p₁(x) = 3x, p2(x) = 2x + x², and p3(x) = B+ax². a) (4 marks) Find the condition on a, ß ER that ensures that {P1, P2, P3} is a basis for P2. (You are free to assume that the polynomials 1, x and x² are linearly independent.) b) (2 marks) In the case ẞ = 1, write the polynomial p(x) = 1 - x - x² combination of P1, P2 and P3. as a linear
Chapter2: Loads On Structures
Section: Chapter Questions
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Transcribed Image Text:3. Let P2 be the vector space of all real polynomials of degree at most 2. Let P1, P2, P3 Є P2 be
given by p₁(x) = 3x, p2(x) = 2x + x², and p3(x) = B+ax².
a) (4 marks) Find the condition on a, ß ER that ensures that {P1, P2, P3} is a basis for P2.
(You are free to assume that the polynomials 1, x and x² are linearly independent.)
b) (2 marks) In the case ẞ = 1, write the polynomial p(x) = 1 - x - x²
combination of P1, P2 and P3.
as a linear
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