9-1 Solving 3 by 3 Systems Day 2

Method 3 – Matrix Elimination It looks a little weird at first, but when you get used to it you might really like this method. Quicker… less paper…more ecofriendly… but more work in your head…

Lets work through a problem 1. We will see at the end of class the example who gets The Gold Star of Clever Thought.  Matrix – a rectangular array consisting of the coefficients and constants of a system of equations.

What happened? Now what? Row 1 times 2 then subtract Row 2 And here? Row 1 minus Row 3 Row 2 times 3 then subtract Row 3

So what did we do? We converted the original system Into this:  which is While it looks long, we did very little work to get down to 3 simple equations that can be back substituted.

Matrix Elimination The coefficients from a 3 by 3 are put it in a matrix and then we work to make a new matrix by multiplying, dividing and/or combining rows. You use elimination method without seeing the variables. That is why it is a little easier – fewer things to keep track of.

The ideal new matrix will have ones on the diagonal and 0’s to the left of the diagonal. Achieved by a)Multiplying or dividing a row by something b)Collecting 2 rows c)Multiplying/Collecting 2 rows. Lets try again together.

Wait….. Please realize this: just as different people will get different intermediate equations with regular elimination, you may not have the same matrix as someone next to you but it doesn’t mean you are wrong. If you have an error, let someone else read follow the problem and see if they can find where the error might be. Also, just aim for the zeroes. In some problems getting the 1 on the diagonals is a mess, so I don’t look for that.

Example