a$)$ Write a function readData which will read in a file called CTEvsT. $x1sx$ and will create $($and return$)$ two

vectors, one called $T($which corresponds to $x$ above$)$ and one vector called CTE $($which corresponds to the

vector $f$ above. Print the vector $T$ and CTE to the command line.

b$)$ Write another function call fitQuadraticFtn. This function will take in the $T$ and CTE vectors of data,

will set up the A matrix, the $f$ vector and solve for the coefficient vector $c.$ It can be shown that the equation

for finding $c$ is given as follows:

$c=(A^{T}A{)}^{-1}(A^{T}f)$ where $c=\left[\begin{array}{c}{c}_1\\ c_2\\ c_3\end{array}\right]$ are the coefficients of the quadratic function that

best fit the data given. This is called a least$-$squares solution and was developed by Gauss.

The function fitQuadraticFtn will return the vector of coefficients $c_1,c_2$ and $c_3.$ Print these out to the

command line.

c$)$ Write a function plotQuadraticFit which takes in the original data points $($T and CTE vectors$)$ along with

the coefficient vector $c$ and creates a plot which shows the original data $($plotted as symbols such as x$\text{'}$s$)$ and

the smooth curve fit. Use $100$ pts to create the smooth plot of the quadratic fit. The final results should look

like Figure $2.$ Display the plot.

Hint: My main program looks like the following. This tells you the function signatures and general structure

of the solution

CTE vs T Data