Maybe I shouldn't have started this blog now, not with everything that's been going on.

Advanced Mathematics, second meeting, fifth week of classes, third trimester: as I promised them last time, I first showed them that it was possible to compute for the values of three variables in three equations using a nine-element matrix (not of a single row or column, thus square) by making any corner triangle off the main diagonal all zero.

The important part was not to start with one element of a particular row or column then go to another row AND column immediately, otherwise the previously changed value will now be non-zero.

Afterwards I demonstrated getting the inverse (and thus the adjoint and determinant) of a three by three matrix.

I made the example interactive just to be sure that the students (all eight of them) knew all the steps in solving for the inverse.

It was a relief to see one of the students who was perennially absent before the first exam, and thus stumbled over the questions concerning solving for the determinant of higher order matrices, now knew exactly how to get the cofactor of certain elements.

And to be perfectly clear, we also computed for the product of the original matrix and its inverse, just to prove that it would be the same as an identity matrix.

Looking ahead to the next lesson in that class, it’s another relatively complex method for getting the solutions of linear equations.

In my mechanics classes for the second meeting of the fifth week of classes, I returned to them the papers of their first quiz.

The most common mistakes they made in the test, I noticed, were using equations for constant acceleration in constant velocity (without equating initial and current velocity, and without setting the acceleration to zero), incorrect conversion factors (ex. 1 kilometer = 100 meters), not showing all the steps (making me suspicious about what seatmate’s paper they got the final answer from), not specifying the units (thus neglecting to convert sometimes) and not enclosing their final answers in a box.

So I started out the discussion with giving them tips on problem solving, as in determining which equations (already provided) to solve based on certain analysis they make about the assigned values (which made it important to identify all the mentioned quantities first).

I included the fact that if force, any sort of vertical motion or two velocities are mentioned (or when the object is at rest or stopped) then definitely we are dealing with acceleration.

I also made a flowchart showing how all the quantities could be used to solve for others, such as forces to get summation of forces, that and mass to get acceleration, and from there to get either initial or current velocity, time or displacement.

I’ll continue this discussion next time, as with talking about our newly hired student assistants. For now, class dismissed.