Let B be the basis P 3 consisting of the Hermite polynomials 1 , 2...

Mollie Wise

Mollie Wise

Answered

2022-11-23

Let B be the basis P 3 consisting of the Hermite polynomials 1 , 2 t , 2 + 4 t 2 and 12 t + 8 t 3 ; and let p ( t ) = 1 + 16 t 2 8 t 3 . Find the coordinate vector of p relative to B.
[ p ] B = [ 7 6 4 1 ]

Answer & Explanation

tezeuszxcL

tezeuszxcL

Expert

2022-11-24Added 14 answers

Let p ( t ) = a .1 + b ( 2 t ) + c ( 2 + 4 t 2 ) + d ( 12 t + 8 t 3 ) = ( 8 d ) t 3 + ( 4 c ) t 2 + ( 2 b 12 d ) t + ( a 2 c ) 8 t 3 + 16 t 2 + 1 = ( 8 d ) t 3 + ( 4 c ) t 2 + ( 2 b 12 d ) t + ( a 2 c ) { 8 d = 8 4 c = 16 2 b 12 d = 0 a 2 c = 1 { d = 1 c = 4 b = 6 a = 9
So [ p ] B = [ 9 6 4 1 ]

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