Solve the problem.
-Let $\mathrm { V }$ be in $\mathrm { P } _ { 4 }$, involving evaluation of polynomials at $- 5 , - 3,0,3$, and 5 , and view $\mathrm { P } _ { 2 }$ by applying the Gram-Schmidt process to the polynomials $1 , t$, and $t ^ { 2 }$.
A) $\mathrm { p } _ { 2 } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } - \frac { 68 } { 5 }$
B) $\mathrm { p } _ { 2 } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } - \frac { 18 } { 5 }$
C) $\mathrm { p } _ { 2 } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } - 10$
D) $\mathrm { p } _ { 2 } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } + \frac { 68 } { 5 }$

Question

Quizplus · Accepted Answer

The correct answer is A because the Gram-Schmidt process orthogonalizes the polynomials with respect to the inner product $\langle f,g\rangle=\int_{-5}^5 f(t)g(t)dt$.

Solve the Problem V\mathrm { V }V Be In P4\mathrm { P } _ { 4 }P4​

Solve the Problem $\mathrm { V }$ Be In $\mathrm { P } _ { 4 }$