(07-12-2018 02:39 PM)sasa Wrote: (07-12-2018 01:37 PM)Joe Horn Wrote: Answer for you: Because Prime's CAS knows more math than Joe Average does, and can do it a lot faster than Joe Average using paper and pencil.

One particular part where CAS may choose longer path may be following:

Find determinant of:

While student may have idea to transform by simply subtracting it to:

... and then easily apply rule that determinant is zero if two columns or rows are equal (or proportional), CAS may run into LU decomposition complexity or standardized path of elimination, which certainly would not be a benefit for a Joe which should learn some shortcuts/tricks (which actually comes from basic rules) in order to perform the task with pencil and paper better and faster than calculator, especially with any larger similar singular matrix, actually making it to develop affection to math, not to blindly use calculator and use to its abilities or flaws.

I do not have any CAS capable calculator to claim upper, however I would be supprised that any calculator can calculate upper determinant with only one described step.

The beauty behind solving some problems is that solution is easy and fast accomplished by spark of an idea, avoiding all complexity standardize approaches may involve.

Prime virtual calc found this:

DET([[1,2,3],[4,5,6],[7,8,9]]); // ==> 0

In this much time:

TEVAL(det([[1,2,3],[4,5,6],[7,8,9]])); // ==> 0_s

Student is still waiting for spark of an idea ...