Question

Find the change of coordinates matrix P from the basis B = {1 + 2t, 2 + 3t} to the basis C = {t, 1 + 5t} of P1

Answer 1

a. find the change of coordinates matea's p from the basis B={ 2424, 2+3*} to the Bass's C-{t,1+2+} of P, Solution : Let denote the based of B by be and be and basis of c by C, and a bea :54] [3] abza Gia 2 [ i Je po- [ i Hence ~ لا 0 12 2 3 P Pense [top 1928) [Co]p 2 a [2] at an 1 3 A + 20 X2 If de 29, + 392 де са esolue these equation by Augmented matrix Subtract 1-09, -29,7 +(392-492) Is -92 92= -1 g a-2 Heuce [C3Jp = [3] Now (62)p: et dare 3 [+] = d[] – Ike Augmented unatre's 1 2 : 2 3:2

R2 2R, o Re 1 12 [1] O: 1.0 [ Jl [6] dz d2=0,1 fence [ CzJp de= o ܕܢ eso, coordinate materie B toe is Pe-sc = [60],[4.06]: [ió] be wolutions
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