Sparse In$-$diagonal matix, F$.$ All enhies not shown are zero, $0$

This question requires you to write MATLAB code to generate the matrix $F$ above.

$($a$)$ In code, generate a matrix $F$ of dimensions $nn$ that is populated with zeros. You will necd to as the user to input the variables $m$ and $n$ which are the dimensions of $F.$

$($b$)$ In your code, use a while loop to that verify that $m$ and $n$ are:

$($i$)$ Whole numbers.

$($ii$)$ Non$-$negative

$($iii$)m=n$

$($i$.$ e$.$ the matrix is square$)$

$($c$)$ Use a nested for loop and an if statement, populate the matrix lo look like the matrix $F$ above.

Hint: Use i and $j$ as counrers and look at the relationship benveen i and $j$ for the elements you intend io have values $-1$ and $2.$

Note: Remenber, where there is $\text{'}$no value' shown in the matix F$.$ there is a zero. Please use MATLAB when answering this.