Problem 44948. Calculate a Damped Sinusoid

I think i need explanation for this concept :
The vector t should be linearly spaced from 0 to T, with N elements.
if I do, a = 1:6, the ans is 1 2 3 4 5 6
but now if i do, a = 1:2:6, ans is 1 3 5
so for linear distributed vector to reach end point 6, we need to do,
a = 1:(6-1)/(6+1):6 --------similarly can it be done as t = 0:(T-1)/(T+1):T? what is the concept in the words 'linearly spaced'?

From the equation y = A.ⅇ^(-λt)*cos(2πft), it might be confused if you don't know the character between A and -λt is the 'euler number'.

I think it is not correctly presented. It should have been re phased or underlineing the fact, that there is no matrix multiplication in the exponent.