Problem #$3.(25$ points$).$ Given the data set $(9\mathrm{.}0,300),(10,375),$ and $(11,425),$ find a $2^{nd}-$order polynomial of the

form $P_n(x)=a_0+a_{1}x+a_2{x}^2$ using the Direct Approach; that is$,$ evaluate the conditions $y_i=P_n(x_i)$ where $n=2.$

Hint: After evaluation of the conditions $y_i=P_n(x_i)$ for each of the data points $(x_i,y_i),$ you should find a linear system

of equations of the form:

$a_0+a_1{x}_1+a_2{x}_1^2=y_1$

$a_0+a_1{x}_2+a_2{x}_2^2=y_2$

$a_0+a_1{x}_3+a_2{x}_3^2=y_3$

$(5$ points$).$ Write the elements of the matrix corresponding to:

a$.$ The matrix of coefficients $[$A$],$

b$.$ The vector of unknowns $\{x\}$ and,

c$.$ The independent terms column vector $\{b\}.$

$(10$ points$).$ Use the Gauss$-$Jordan elimination method to solve the resulting system of linear simultaneous

equations. Show all the steps of the computation.

$(5$ points$).$ Write the resulting $2^{nd}-$order polynomial and find the value of $y(9\mathrm{.}5).$

$(5$ points$).$ Verify your results by substituting $\{x\}$ into each equation given in Eq$.(2).$