Carl Horowitz

**University of Michigan**

Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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So for this particular matrix, what we have is the coefficients from x, y and the answer in one row and the x, y and the answer in another and for augmented matrix we typically drew that little dotted line down the middle to separate our variables from our answer.

So now what we're going to do is use our calculator to simplify this up. So to put in our augmented matrix, what we need to do is go to the matrix option in our calculator and we get there by going to second matrix which is the x and -11, so then we scroll over to edit and this list of ABC so on and so forth are just the names that your calculator gives matrices.

So pick any of them typically A is going to be the easiest and then the first thing we get into it says matrix A 1 by 1. This is the dimensions for our matrix and what it has is it's rows by columns so what we end up with is for our matrix, we have two, rows and 3 columns, hit enter in between and up here is our 2 by 3 matrix.

So then we just go down the row entering our info so we have the number 1, then we have -3 and be careful when you're entering -3 that you don't put the minus sign. The minus sign will give you an error so make sure you go to the negative sign which is next to the decimal button. So you put in -3, hit enter and then our last one is -7, hit enter again we go to our second row where we had the entries, entry is 2, 2 and 10.

So once we have inputted all of our information, we can then quit the matrix stuff, so just go to second mode or quit it. Then we go back to our matrices, so this is the second matrix and what we want to do is scroll over to the Math option and if we scroll down what you end up seeing are these two options. One that says rref and one that says ref. The ref is row echelon form and the rref is row reduced echelon form. So depending on which units you've studied, you can use either of these options.

So we are going to first do say row echelon form. So once you're on A, hit enter and the ref comes up, then hit second matrix, throw in the matrix that you created so A and then close your parenthesis and click enter and what comes up is a matrix is row echelon form. So what we have here is y is equal to 3, that from that bottom row, we can take that and plug it back into the top equation to solve it out completely.

What we can also do is row reduced echelon form which is basically the same process so we go to second matrix over to Math and this time we are going to go down to rref function. When we get there hit enter then go back to second matrix throw in A, throw in our n parenthesis, hit enter and what we have here is in row reduced echelon form where this tells us straight up what x value is and our y value is.

So solving a system of linear equations using matrices. First you make your augmented matrix this can either work for a 2 by 2 equation in two variables or three variables or even 4 so on and so forth, but you make your matrix and then you use the function of row echelon form or row reduced echelon form in order to solve it out.