Create list of elements with dependence on a variable

Question

I'm aware that we can make a list of elements:

x = Table[Symbol["x" <> ToString@i], {i, n}];

This returns x = {x1,x2,x3} when n = 3. What I want is to be able to turn each of these variables x1,x2,x3 into functions of t (e.g. I want y = {x1[t],x2[t],x3[t]}).

Any ideas would be appreciated.

Answer 1

Indexed variables are usually much easier to work with.

Format[x[n_Integer]] := Subscript[x, n]

Format[a[n_Integer]] := Subscript[a, n]

X[t_, n : _Integer?Positive : 3] := Array[x[#][t] &, n]

Using default value for n

X[t]

Specifying a value for n

X[t, 5]

X[t, 5].Array[a, 5]