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real coefficients. Let p1(t) = 1–t+t², p2(t) = 2t – 3t², p3(t) = -1+t+2t² be elements of V. (a) Are p1(t), p2(t), p3(t) linearly independent in V? Why or why not? (b) Are p1(t), p2(t), p3(t) a basis of V? Why or why not?

real coefficients. Let p1(t) = 1–t+t², p2(t) = 2t – 3t², p3(t) = -1+t+2t² be elements of V. (a) Are p1(t), p2(t), p3(t) linearly independent in V? Why or why not? (b) Are p1(t), p2(t), p3(t) a basis of V? Why or why not?

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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Let V = P2(R) be the space of polynomials of degree at most 2 with
Transcribed Image Text:Let V = P2(R) be the space of polynomials of degree at most 2 with
real coefficients. Let p1(t) = 1–t+t², p2(t) = 2t – 3t², p3(t) = -1+t+2t² be elements of V. (a) Are p1(t), p2(t), p3(t) linearly independent in V? Why or why not? (b) Are p1(t), p2(t), p3(t) a basis of V? Why or why not?
Transcribed Image Text:real coefficients. Let p1(t) = 1–t+t², p2(t) = 2t – 3t², p3(t) = -1+t+2t² be elements of V. (a) Are p1(t), p2(t), p3(t) linearly independent in V? Why or why not? (b) Are p1(t), p2(t), p3(t) a basis of V? Why or why not?
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