Let A and C be the following ordered bases of P3(t): A = (1, 1 + t, 1 + t + t^2, 1 + t + t^2 + t^3) C = (1, -t, t^2 -t^3) Find tha change of coordinate matrix I_{CA}

ringearV 2021-02-14 Answered
Let A and C be the following ordered bases of P3(t): A=(1,1+t,1+t+t2,1+t+t2+t3)
C=(1,t,t2t3) Find tha change of coordinate matrix ICA
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irwchh
Answered 2021-02-15 Author has 102 answers

Solution: A=(1,1+t,1+t+t2,1+t+t2+t3)andC=(1,t,t2,t3) To find the chance of coordinate matrix ICA:
1=a1(1)+a2(1+t)+a3(1+t+t2)+a4(1+t+T2+t3)
a1+a2+a3+a4=1,a2+a3+a4=0,a3+a4=0anda4=0
a1=1
t=b1(1)+b2(1+t)+b3(1+t+t2)+b4(1+t+t2+t3)
Ri>owb1+b2+b3+b4=0,b2+b3+b4=1,b3+b4=0andb4=0
b1=1andb2=1
t2=c1(1)+c2(1+t)+c3(1+t+t2)+c4(1+t+t2+t3)
c1+c2+c3+c4=0,c2+c3+c4=0,c3+c4=1andc4=0
c2=1,c3=1

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