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Q3 3 Points In the vector space V = P₂ of all polynomials of degree at most 2, consider the elements Pi(t)=1+t, P2(t) = 1-t, Ps(t)=1+2t+t². Determine if it is possible to write the polynomial q(t) = t² as a linear combination of Pi(t), p2(t), ps(t). If possible, show which linear combination of p₁(t), p2(t), ps(t) is equal to q(t) . If not possible, explain why. Show all of your work. Please select file(s) Select file(s) Save Answer

Q3 3 Points In the vector space V = P₂ of all polynomials of degree at most 2, consider the elements Pi(t)=1+t, P2(t) = 1-t, Ps(t)=1+2t+t². Determine if it is possible to write the polynomial q(t) = t² as a linear combination of Pi(t), p2(t), ps(t). If possible, show which linear combination of p₁(t), p2(t), ps(t) is equal to q(t) . If not possible, explain why. Show all of your work. Please select file(s) Select file(s) Save Answer

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 12E
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Q3 3 Points In the vector space V = P₂ of all polynomials of degree at most 2, consider the elements Pi(t)=1+t, P2(t) = 1-t, Ps(t)=1+2t+t². Determine if it is possible to write the polynomial q(t) = t² as a linear combination of Pi(t), p2(t), ps(t). If possible, show which linear combination of p₁(t), p2(t), ps(t) is equal to q(t) . If not possible, explain why. Show all of your work. Please select file(s) Select file(s) Save Answer
Transcribed Image Text:Q3 3 Points In the vector space V = P₂ of all polynomials of degree at most 2, consider the elements Pi(t)=1+t, P2(t) = 1-t, Ps(t)=1+2t+t². Determine if it is possible to write the polynomial q(t) = t² as a linear combination of Pi(t), p2(t), ps(t). If possible, show which linear combination of p₁(t), p2(t), ps(t) is equal to q(t) . If not possible, explain why. Show all of your work. Please select file(s) Select file(s) Save Answer
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