Feb 2024 Update: Refer to P2 with the inner product given by evaluation at 1, 0, and 1. Compute (p,q), where p(t) 6-t,

Question

Refer to P2 with the inner product given by evaluation at 1, 0, and 1. Compute (p,q), where p(t) 6-t, q(t) = 3 +2t2. (p.q)

Asked By FrostyMoonlight95 at 01 Feb 2024

Answered By Expert

Abraham

Expert · 3.7k answers · 3k people helped

Step 1/2

Given that `mathbbP_2` , with the inner product given by evaluation at `-1,0, and 1.`Hence we have `<<p,q>>=p(-1)q(-1)+p(0)q(0)+p(1)q(1)` .`p(t)=6-t quad, quad q(t)=3+2t^2``p(t)=6-t implies p(-1)=7, p(0)=6,p(1)=5``q(t)=3+2t^2 implies q(-1)=5,q(0)=3, q(1)=5`

Step 2/2

Hence we have,

`<<p,q>>=p(-1)q(-1)+p(0)q(0)+p(1)q(1)``implies <<p,q>>=(7)(5)+(6)(3)+(5)(5)` .... ( By putting all values)`implies<<p,q>>=35+18+25=78`

Therefore we have,

`<<p,q>>=78`

Final Answer

Final answer is given below:

`<<p,q>>=78`

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