In Matlab, solve the 'Eva' problem. Obtain the matrix $R$ from the file ps$2\_$R$.$mat from

the course website; download it and save it in whatever folder Matlab is running in$,$ and

load it by typing load ps$2\_$R at the prompt in the Matlab command window. This

creates a variable called $R$ in the Matlab environment that you can use for subsequent

statements. Take $r_p=1\mathrm{.}1($i$.$e$.,$ desired return of $10\%).$ Follow the steps described on

Slide $7$ of file M$08,$ which were also presented in lecture. At the end of the procedure,

exhibit the vector $x_{*}.$ Hand in a copy of the command window that shows each step. If

you use a script, hand in the listing of the script and the output. You can also choose

to write a function $($not required$)$; in this case, hand in the function listing and a test

run.

Here are some features of Matlab needed for this question:

If $A$ is a matrix, then ${\displaystyle \underset{?}{\overset{?}{}}}(A,1)$ returns a row vector that is the sum of the rows

of A$.($Similarly$,$ sum $(A,2)$ returns a column vector that is the sum of the columns

of A$.)$

To make an $mn$ matrix of all $1\text{'}$s$,$ use $A=$ones$(m,n)$;$.$ This statement generates

a row vector if $m=1$ or a column vector if $n=1.$ There is an analogous function

for all $0\text{'}$s called zeros.

Matrix transposition in Matlab is indicated with an apostrophe symbol: A$2\text{'}$

means $A_2^T.$

Put trailing semicolons on statements to avoid displaying the result of each step

in the command window. Omit them to display the result.

Multiplication $($matrix$-$matrix, matrix$-$vector, and scalar$)$ is denoted with an as$-$

terisk, e$.$g$.,$ the statement bbar$=$A$1*$x$0$; multiplies $A_1$ and $x_0,$ and assigns the

result to $\frac{?}{\text{b}\text{a}\text{r}}(b).$

To apply a matrix inverse to a vector, use the $\frac{\frac{?}{?}}{?}$ operation, which solves a linear

system. For example, to compute $(R_2^{-T}b)$ in Matlab, you would use the expression:

$(($R$2\text{'})\backslash$b$).$

To extract submatrices, use the colon notation. For example, the statement

$[$Qtilde$,$Rtilde$]=$qr$($Abar$)$; followed by Ybar$=$Qtilde$($:$,1$:$8)$; sets $\frac{?}{\text{b}\text{a}\text{r}}(Y)$ to the

first eight columns of the Q factor in the QR $-$factorization of $\frac{?}{\text{b}\text{a}\text{r}}(A).$