WordPress has been acting a bit flaky the last couple days. Hopefully that will settle down.
I don’t quite understand yet why my Tuesday-Thursday classes all start at nice, round, on-the-hour times, but my Monday-Wednesday-Friday classes are at weird intervals. You’d think it would be the opposite.
For instance, this morning I showed up for my 9:00 math class, and was five minutes or so ahead of time. Started to open the door, noticed a whole class full of people eanestly plugging away. No problem. At 9:00, however, none of them had left, nor was there any sgn the class was breaking up yet. At this point my brain, ever helpful, suggested that I’d read the clock wrong an was a full hour late, and had missed the whole class. This has happened before.
However, more sane reflection let me remember that this class starts at 9:10, not 9:00. Everything worked out fine. This has not stopped me from thinking of this class as a 9:00 class.
Back to matrices.
Discussed Row Echelon Form last time. Talked about Reduced Row Echelon Form today. Basically row echelon, but with the extra step of reducing every equation to having only one non-zero coefficient.
Using the Gauss-Jordan Method to Put a Matrix into Row Echelon Form (or Diagonal form)
- Obtain 1 as the first element of the first row.
- Use the first row to transform the remaining entries in the first column to 0.
- Obtain 1 as the second entry in the second row.
- Use the second row to transform the remaining entries in the second column to 0
- Continue in this manner until all but last column have been transformed to 1 and zeros.
The major benefit of reduced row echelon form is avoiding finding a point of intersection algebraically. Instead of finding one value and substituting it back into previous equations, you eliminate all but one value from each equation.