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(2.3) Let pi = 2-x+x²,p2 = 1+x, p3 = x+x². Show that S = {p1. P2, P3} spans P2. Conclude that S is a basis for P2. (2.4) Using (2.3) or otherwise, write p = 3+5x-4x2 as a linear combination of p1, P2 and p3. Show all working. Hence find (p)s, the coordinate vector of p relative to S. (2.5) Explain why are the vectors q1 = 8+ 4x - 6x2 and q2 = -4 – 2x + 3x2 are linearly dependent in P2?

(2.3) Let pi = 2-x+x²,p2 = 1+x, p3 = x+x². Show that S = {p1. P2, P3} spans P2. Conclude that S is a basis for P2. (2.4) Using (2.3) or otherwise, write p = 3+5x-4x2 as a linear combination of p1, P2 and p3. Show all working. Hence find (p)s, the coordinate vector of p relative to S. (2.5) Explain why are the vectors q1 = 8+ 4x - 6x2 and q2 = -4 – 2x + 3x2 are linearly dependent in P2?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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TelkomSA 2G 10:01 AM Vodacom SA You Just now Question 2 In this question we are considering the vector space P2, which is the collection of all polynomials of degree <3.
Transcribed Image Text:TelkomSA 2G 10:01 AM Vodacom SA You Just now Question 2 In this question we are considering the vector space P2, which is the collection of all polynomials of degree <3.
TelkomSA © 2º| ll 100% 4G 9:59 AM Vodacom SA You Just now (2.3) Let pi = 2-x+a2, p2 = 1+x,p3 = x+x?. Show that S = {p, P2, P3} spans P2. Conclude that S is a basis for P2. (2.4) Using (2.3) or otherwise, write p = 3+ 5x – 4x2 as a linear combination of Show all working. Hence find (p)s, the coordinate vector of p relative to S. P1: P2 and P3- (2.5) Explain why are the vectors q1 = 8+ 4x - 6x2 and q2 = -4- 2.x + 3x2 are linearly dependent in P2?
Transcribed Image Text:TelkomSA © 2º| ll 100% 4G 9:59 AM Vodacom SA You Just now (2.3) Let pi = 2-x+a2, p2 = 1+x,p3 = x+x?. Show that S = {p, P2, P3} spans P2. Conclude that S is a basis for P2. (2.4) Using (2.3) or otherwise, write p = 3+ 5x – 4x2 as a linear combination of Show all working. Hence find (p)s, the coordinate vector of p relative to S. P1: P2 and P3- (2.5) Explain why are the vectors q1 = 8+ 4x - 6x2 and q2 = -4- 2.x + 3x2 are linearly dependent in P2?
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