Multiplying an array by a number

Can't say for sure without seeing the sheet (which you if ever possible always should attach and say which Prime version) but it seems to me that you are using the wrong type of index when you define k₀, t₀, u₀, etc. You seem to be using the vector/matrix index ans so you are creating a 1x1 matrix. You should rather use the literal index (keyboard short is Ctrl+-) so the zero is just a subscripted part of the name and not the index of a vector.

Or did you intend to create matrices (arrays)? Then you will have to be more concrete in explaining what exactly is the concern.
If creating arrays was done one purpose but you expected a normal numerical result for u"₀ in your first picture, the reason you get a 1x1 matrix result is the usage of k instead of k₀.

I see no reason for the effect in your second picture unless you somewhere have defined a value for u"₁.

You should:

1. State which version of Prime you are using.

2. Attach the worksheet (.mdcdx file).

3. Realise that there are two kinds of 'things' that result in a sort of subscript:

    a A literal subscript, which you get by typing [Ctrl-_] (That is, depressing the [Ctrl] key and then hitting the [_] key, the 'underscore'). This creates an extension to the variable. Example: variable_subscript.

   b An index (into a vector, a matrix or an array) you get this by typing a "[" (opening square bracket) followed by the index. If you look closely, when the cursor is on the expression with the index, you'll see a faint square bracket.

Now, without your worksheet I have to guess, but my guess is that you've created u₀ using the [, this means that u is a single element vector, and 0 is the index to that (first) element.

The result you get for u'' is a two element vector, where each of the two elements is a one element vector.

Success!
Luc