Matrix function Issues

The way you used the range variables and defined your vector singly is a bit irritating.

You have to be aware that Mathcad would begin the index count of vecors and matrices by 0. Thats the reason your 4-element vectors are 5x1 matrices with the first element set to zero. You should consider that fact and correct your indices accordingly. You can set the system variable ORIGIN to 1 to change that behaviour, but usually its a good idea to leave it at the default value 0.

One way to achieve what you want is the following which does not make use of the range variable j, but uses vectorization. Note that setting w[0 to 1 is only necessary because of the problem described above. If you change your vector definition that would be no longer necessary.

As you aked WHY your way of function definition did not work, here is a short explanation. Basically the key for understanding what happens is the understanding of the difference between vectors and range variables. This was discussed quite a lot here in a multitude of threads and the subject was given a thorough treatise from time to time.

This is what failed in your sheet:

Error: "This value has to be an integer"

and you wondered why, as the same expression seemed to work OK if used on its own:

The reason is that, while the above result looks like a vector, it isn't !!! At least not a normal one you could use as any other vector. The range variable acts as sort of an implicit for-loop and what looks like a result vector is just Mathcads way to present the results of this loop. For some reasons they have decided not to create a normal vector in this situation but a construction which is rather useless for further calculations.

You can see that its not a conventional vector as you are not allowed to assign that expression to a variable

Error: "This value has to be an integer"

nor are you able to access a single element of that construction

Error: "This value has to be a vector"

So one solution is to use Mathcads vectorization operator, which does the looping through the vector elements and creates a new vector as I showed in the last reply. Another way is to use Mathcads programming ability

You could even use j instead of k, but I thought that something like "j element-of j" would be too confusing. The left j would be a loacal variable and the rightmost j would be your worksheet range variable.

What I said in the last post still applies - you should cleanup your worksheet, especially concerning the indexing of matrices and vectors. Most of the time your worksheet is written as if you are not aware that Mathcad starts numbering at zero by default. Only in one definition of the Matrix Cd you have used an index 0 yourself. Not sure if that was done on purpose.

One last example as a conclusion: