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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Some functions are not easily written as a formula. On a graph, a step function looks like a flight of stairs. The graphs of **step functions** have lines with an open circle on one end and a closed circle on the other to indicate inclusion, like number line inequality graphs. A rounding step function tells us to round a decimal number to the next whole integer or the previous whole integer.

Matrices are a new way of organizing data. And so basically what they are, are they are a couple of brackets with a bunch of numbers in them.

And when this is useful is when we just have a number of equations or a number of things we want to organize. We can throw them into different rows a columns and sort of sort it out instead of having to write a whole bunch of information down in formulas or what have you.

And so when we're dealing with Matrices there is a number of things we created to help us talk about them. The first thing that we need to talk about is the dimensions of a matrix, and the dimensions are basically the number of rows by the number of columns, and I just misspelled that number of columns I was never really good in English number of columns.

So looking at our matrix remember columns go up and down think about you know Greece and all the ancient architecture columns are up and down. So columns are the number of columns number of verticals statements rows go side to side. So we have two rows and we have three columns in this instance okay.

Another thing we need to do is if we ever want to specify just one piece of data in this thing, so say now we have here we have six numbers. I just want to talk about this -7. This matrix is name matrix a, so when I say a this is referring to this set of data. And what you can do is say a and then you just do row column, and that will tell you about a specific piece of data. So if I want to talk about this number 7 a it's in the second row that's a two and it's in the third column so this is 3. So a, 2, 3 is referring to -7.

So let's take a look at a couple other Matrices make sure we have this down. So let's say we have Matrice b okay just another set of data 1, 7, 8, and 5. Okay so first we want to see what the dimensions are and dimensions are sometimes just abbreviated DIM just so save a little bit of time. So dimensions are again rows by columns, so how many rows do we have just have one row across so the dimension of this is just one and we have 4 columns 2, 3, 4 so this is a 1 by 4 matrix okay. See if we can get a little bit more information say we say b 1 2. The first row is the only row we have and the second column which is relating to the number 7 okay.

One last example let's talk about matrix c 2, 3, 4, 0, 7, 8, alright so another matrix to dimention this one. So rows by columns three rows across, three columns down so this is a 3 by 3 it's a square matrix just because is same dimension either side and if I ask you for c let's say 2, 1 you're looking at the second row, first column so this is going to be equal to 2. So some very basic language so we can communicate about the Matrices.