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Graphing Calculator: Matrices - Part II
In order to perform operations with matrices, we must first have matrices input into the calculator. We will be working with the following matrices:


For help on inputting matrices in the calculator, click here.

Once the matrices are in your calculator, you are ready to begin performing operations on [A], [B], and [C].

Let’s begin with [A] + [B]. Before adding matrices, you must make sure they have the same dimensions. Addition and subtraction of matrices can only be done with matrices of the same dimensions. To see how to add or subtract matrices by hand, click here.

Now back to [A] + [B]. Since they are both 2 x 2 matrices, we can proceed with adding them.

Make sure you are on your home screen before you go any further.

Access the MATRIX menu with either the MATRIX key on the TI-83 or with the keys on the TI-83 Plus or the Silver Edition. Make sure you are in the NAMES menu.

Select and press . You should see the screen below.



Now press the key. Again, access the MATRIX menu and this time choose from the NAMES menu. Pressing should give you the screen below.



When you press you will see the answer matrix on your screen.



You can ignore the extra brackets around the matrix. They do not effect your answer.

Verify that you will get the same answer if you add [B] + [A].



Although you cannot add [A] + [C], it is interesting to see how the calculator handles the command. Enter [A] + [C] on your home screen as shown below.



Now press and see what happens.



The calculator is letting you know that the dimensions of the two matrices are not the same. Recall that is a 2 x 2 matrix and is a 3 x 2 matrix and cannot be added because the dimensions are not the same.

Now let’s look at multiplication of matrices. When multiplying matrices, the number of columns in the first matrix must match the number of rows in the second matrix. For more explanation of this, see the matrix lesson.

According to the rules of multiplication of matrices, we will be able to multiply [A][B], [B][A], [C][B], and [C][A], but NOT [A][C] or [B][C].

When entering the command on your home screen, you can choose to use the key or not. If you leave out the multiplication symbol, the calculator will assume multiplication.


Now try B][A] and make sure you get the answer below.



Note that the order is important in multiplying matrices. [A][B] gives a different answer than [B][A].

When you multiply [C] (a 3 x 2 matrix) and [A] (a 2 x 2 matrix) your answer will be a 3 x 2 matrix because 3 is the number of rows in [C] and 2 is the number of columns in [A].

Confirm that the answer to [C][A] is the 3 x 2 matrix below.



Make sure you can get the answer shown below for [C][B].



You should also make sure that you get an error message when you try to multiply [A][C].


When a matrix has the same number of rows and columns, it is called a square matrix. Square matrices have an inverse. There are ways to find the inverse of a matrix by hand, but it is very easy for the calculator to compute the inverse.

Since [A] and [B] are both square matrices, let’s find their inverses.

From your home screen, access the MATRIX menu and then from the NAMES menu, choose and press .



Now use the key so that your screen looks like the one below.



When you press , you should see the answer below.



My calculator has been set at two decimal places in the MODE setting so that the decimal values are all visible on my screen. For information on how to change your MODE settings, click here.

Make sure you can find the inverse of [B] as shown below.

 



S Taylor

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