Both B= {1, cost,cos t,cos' t} and C={1,cost,cos 2t, cos 3t} are bases of a vector space H = Span{l, cost,cos t,cos t}. Assume the following trigonometric identities. cos 21 =-1+2 cos?t cos 3t =-3 cost+4cos't a) Find the transition matrix P-3 · b) Find the transition matrix Pc

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Both B= {1, cost,cos? t,cos' t} and C={1,cost,cos 2t, cos 3t} are bases of a vector
space H =Span{1, cost,cos t,cos t}. Assume the following trigonometric identities.
cos 2t =-1+2 cos? t
cos 3t = -3 cost+4cos³ t
a) Find the transition matrix Pc-B •
b) Find the transition matrix PC
(4 cos t-2 cos't)dt, then compute the
c) Use matrix Pe-x or P-c to transform the integral
BC
integral.
Transcribed Image Text:Permanent Both B= {1, cost,cos? t,cos' t} and C={1,cost,cos 2t, cos 3t} are bases of a vector space H =Span{1, cost,cos t,cos t}. Assume the following trigonometric identities. cos 2t =-1+2 cos? t cos 3t = -3 cost+4cos³ t a) Find the transition matrix Pc-B • b) Find the transition matrix PC (4 cos t-2 cos't)dt, then compute the c) Use matrix Pe-x or P-c to transform the integral BC integral.
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