A symmetric tridiagonal matrix A can have nonzero values at only diagonal elements and elements just below or above diagonal elements. Also A$^$T$=$A due to the symmetry. For example,

A$=((2100$@$1210$@$0121$@$0012))$

is an n by n symmetric tridiagonal matrix with n$=4,$ the diagonal elements d$=2,$ and the non$-$diagonal elements a$=1.$

Write a MATLAB function A$=$symTri$($n$,$d$,$a$)$ to return such an n by n matrix A with the same diagonal values d and nondiagonal values a$.$

Use no special built$-$in functions.

Make an empty matrix A first. All the elements are zeros right after its creation.

For efficiency, your program should update the necessary elements only, i$.$e$.,$ do not rewrite a zero into another zero.

Include your $.$m script file in the zip file.

What is the asymptotic running time of your algorithm? Your answer should be O$($f$($n$))$ for a simple function f$($n$)$ of n$.$ Briefly justify your answer regarding a substitution A$\_($i$,$j$)$x as one floating point operation A$\_($i$,$j$)0+$x$.$