Write a function file, M $=$ TriDiagonalMatrix $($n$),$ that takes input arguments of an integer n and

returns a square matrix of size n where the first and last rows are zeros and the middle rows $(2,3,..,$n$-1)$ are constructed according to the pattern defined in the following examples.

M $=$ TriDiagonalMatrix$(3)$

M $=[000$;$246$;$000]$

M $=$ TriDiagonalMatrix$(5)$

M $=[00000$; $24600$;$036900$; $004812$;$00000]$

M $=$ TriDiagonalMatrix$(10)$

M $=[0000000000$;$2460000000$;$0369000000$;$00481200000$;$000510150000$;$000061218000$;$000007142100$;$000000816240$;$000000091827$; $0000000000]$

Your function must perform the following

$1.$ Pre$-$allocate the output parameter M to the appropriate size.

$2)$ Use a loop to modify the values in the middle rows $(2,3,...,$ n$-1).$

$3.$ If the input parameter n is less than $3,$ assign M a value of NaN.

This is done in MATLAB. This is code I tried earlier but doesn't work according to the test codes I have.

function M $=$ TriDiagonalMatrix$($n$)$

if n $<3$

M $=$ NaN;

return;

end

M $=$ zeros$($n$)$;

for i $=2$:n$-1$

M$($i$,$ i$-1)=$ i$-1$;

M$($i$,$ i$)=$ i;

M$($i$,$ i$+1)=$ i$+1$;

end

end

If possible, can you try to include the $3$ by $3,5$ by $5,$ and $10$ by $10$ matrices inside the code instead of the $"$i$"$ notation I used?