Let gamma = {t^2 - t + 1, t + 1, t^2 + 1} and beta = {t^2 + t + 4, 4t^2 - 3t + 2, 2t^2 + 3} be ordered bases for P_2(R).Find the change of coordinate matrix Q

e1s2kat26 2020-11-01 Answered

Let γ={t2t+1,t+1,t2+1}andβ={t2+t+4,4t23t+2,2t2+3}beorderedbasesforP2(R). Find the change of coordinate matrix Q that changes β coordinates into γ coordinates

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Expert Answer

i1ziZ
Answered 2020-11-02 Author has 92 answers

Let t2+t+4=γ1(t2t+1)+γ2(t=1)+γ3(t2+1)
γ1+γ3=1,γ1+γ2=1,γ1+γ2+γ3=4
1+γ2=4
γ2=3
γ1+γ2=1γ1+3=1γ1=2
γ1+γ3=12+γ3=1γ3=1 Let 4t23r+2=γ1(t2t+1)+γ2(t+1)+γ3(t2+1)
γ1+γ3=4,γ1+γ2=3,γ1+γ2+γ3=2
4+γ2=2
γ2=2
γ1+γ2=3γ12=3γ1=1
γ1+γ3=41+γ3=4γ3=3 Let 2t2+3=γ1(t2t+1)+γ2(t+1)+γ3(t2+1)
γ1+γ3=2,γ1+γ2=0,γ1+γ2+γ3=3
2+γ2=3
γ2=1
γ1+γ2=0γ1+1=0Ri>owγ1=1
γ1+γ3=21+γ3=2γ3=1

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