Using Matrices on the TI-83/84 calculator

Disclaimer: The same rules apply to using the calculator as doing it on paper. Add/minus, same size. Multiplying matrix x matrix, 1^st matrix’s columns must be same number as 2^nd matrix’s rows.

To use matrices on your claculator you must know a couple quick steps.

1) You must Know how to enter the Matrix Function screen. ( [2^ND] [x^-1] )

2) How to clear your calculators memory. ( [2^ND] [+] [7] [1] [2] [ENTER] )

Before we start you should all quickly clear your calculators memory.

Editing the Matrices

Now to begin, first enter the Matrix Function screen.

Once you enter the Matrix Function screen, on the top bar you should be over NAMES.

Go right twice, now you should be hovering over EDIT, use the [▲] and [▼] to highlight the matrix you want to edit. (A-J) and hit [ENTER].

Now you are in the matrix editing screen, on the top right hand side are the dimensions, and below that is you current matrix. You should start off with a 1 x 1 matrix. Your screen should look something like this.

MATRIX [x]         1              x     1

[0                                            ]

In this screen you want to edit the dimensions move your cursor over the number you would like to change, press the number you want to input as the dimension, then hit [ENTER].

After you have set your dimensions to what you want it’s time to edit your matrix. For my example I will use a 2 x3 matrix in the [A] slot. With the blank matrix without anything put in it should look like this.

MATRIX [A]        2              x     3

[0            0              0              ]

[0            0              0              ]

To input numbers into the matrix you simply highlight the number you want to edit, put in the number you want then hit [ENTER].

Say for this matrix I want to input the numbers 6, -7, and 18 in the first row, I would simply highlight the number in the first position, punch in 6 and hit [ENTER]. After you hit enter it will automatically jump to the next number, so I would punch in -7 then hit [ENTER], and do the same for 18. Then the matrix would look something like this.

MATRIX [A]        2              x     3

[6            -7            18           ]

[0            0              0              ]

Now follow the same steps and before but highlighting the second row but with the numbers that belong in the corresponding positions, say for this matrix those numbers are 5, -9, and 23. After we input these numbers the matrix should look something like this.

MARTRIX [A]      2              x     3

[6            -7            18           ]

[5            -9            23           ]

Now we have completed making a matrix on the calculator. Lets quickly make two other matrices to show how to do the math, let’s call them [B] and [C].

MATRIX [B]         2              x     3

[8            12           -8            ]

[-4          8              14           ]

MATRIX [C]         3              x     2

[12          10           ]

[8            9              ]

[7            6              ]

Before you start trying to do the math, make sure you quit out of the matrix editing by pressing [2^ND] [MODE].

Matrix Math

Now that we have some matrices to use lets learn how to do the math on the calculator, the math that I will be doing is based off the TI-84 plus, so if you have a different model and the process is different I am sorry for your inconvenience.

First up is addition, for addition all you need to do is enter the Matrix Function screen and select the first matrix that you want to add, press the [+] button on your calculator, then re enter the Matrix Function screen and select the second matrix you want to add then hit [ENTER]. For the sake of demonstration is shall add [A] and [B]. So to add [A] and [B] together you would need to press [2^ND] [x^-1] [ENTER] [+] [2^ND] [x^-1] [▼] [ENTER] [ENTER]. After that our screen should look something like this.

[A] + [B]

                [[14     5      10]

                 [1     -1     37]]

Follow the same steps except substitute [+] with [-] and you can do subtraction. ([2^ND] [x^-1] [ENTER] [-] [2^ND] [x^-1] [▼] [ENTER] [ENTER].) If you subtract your screen should look like this.

[A] – [B]

                [[-2     -9       26]

                  [9      -17     9]]

Scalar multiplication is fairly easy, for example I’ll do a multiply [C] by 1.12. To do so you need to press [1] [.] [1] [2] [2^ND] [x^-1] [▼] [▼] [ENTER] [ENTER]. After that your screen should look like this.

1.12[C]

[[13.44   11.2]

 [8.96     10.08]

[7.84      6.72]]

Now for the final type of multiplication, multiplying one matrix by another.

This is simply achieved by swapping out the [+] button with the [X] button. So I will multiply [A] and [C]. ([2^ND] [x^-1] [ENTER] [X] [2^ND] [x^-1] [▼] [▼] [ENTER] [ENTER].) After you multiply the two matrices your screen should look like this.

[A] * [C]

                [[142     105]

                  [149     107]]