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Matrix Concepts -- Matrices on Calculators

Module by: Kenny M. Felder. E-mail the author

Summary: This module explains using and solving matrices on a calculator.

Many modern graphing calculators have all the basic matrix operations built into them. The following is a brief overview of how to work with matrices on a TI-83, TI-83 Plus, TI-84, or TI-84 Plus.

The calculator has room to store up to ten matrices at once. It refers to these matrices as [A], [B], and so on, through [J]. Note that these are not the same as the 26 lettered memories used for numbers.

The following steps will walk you through the process of entering and manipulating matrices.

  1. Hit the MATRX button. On a TI-83, this is a standalone button; on a TI-83 Plus, you first hit 2nd and then MATRIX (above the x–1x–1 button). The resulting display is a list of all the available matrices. (You have to scroll down if you want to see the ones below [G].)
    Figure 1
    A graph of menu from a TI-83 graphing calculator.
  2. Hit the right arrow key ► twice, to move the focus from NAMES to EDIT. This signals that you want to create, or change, a matrix.
    Figure 2
    A graph of menu from a TI-83 graphing calculator.
  3. Hit the number 1 to indicate that you want to edit the first matrix, [A].
  4. Hit 4 ENTER 3 ENTER to indicate that you want to create a 4x3 matrix. (4 rows, 3 columns.)
    Figure 3
    Screenshot of a TI-83 graphing calculator displaying a 4x3 matrix.
  5. Hit
    
    1  ENTER 2  ENTER 3  ENTER
    4  ENTER 5  ENTER 6  ENTER
    7  ENTER 8  ENTER 9  ENTER
    10 ENTER 11 ENTER 12 ENTER
    This fills in the matrix with those numbers (you can watch it fill as you go). If you make a mistake, you can use the arrow keys to move around in the matrix until the screen looks like the picture below.
    Figure 4
    Screenshot of a TI-83 graphing calculator displaying a 4x3 matrix.
  6. Hit 2nd Quit to return to the main screen.
  7. Return to the main matrix menu, as before. However, this time, do not hit the right arrow to go to the EDIT menu. Instead, from the NAMES menu, hit the number 1. This puts [A] on the main screen. Then hit ENTER to display matrix [A].
    Figure 5
    Figure 5 (graphics5.png)
  8. Go through the process (steps 1-7) again, with a few changes. This time, define matrix [B] instead of matrix [A]. (This will change step 3: once you are in the EDIT menu, you will hit a 2 instead of a 1.) Define [B] as a 3x2 matrix in step 4. Then, in step 5, enter the following numbers:
    10 40 20 50 30 60 10 40 20 50 30 60 size 12{ left [ matrix { "10" {} # "40" {} ## "20" {} # "50" {} ## "30" {} # "60"{} } right ]} {}
    (1)
    When you are done, and have returned to the main screen and punched 2 in the NAMES menu (step 7), your main screen should look like this:
    Figure 6
    Screenshot of a TI-83 graphing calculator displaying a 4x3 matrix.
  9. Now, type the following keys, watching the calculator as you do so. TI-83 Plus users should always remember to hit 2nd MATRIX instead of just MATRX. MATRX 1 + MATRX 2
    Figure 7
    Screenshot of a TI-83 graphing calculator displaying a 4x3 matrix and the resulting sum of adding matrices A & B.
    This instructs the computer to add the two matrices. Now hit ENTER
    Figure 8
    Screenshot of a TI-83 graphing calculator.
    Hey, what happened? You asked the computer to add two matrices. But these matrices have different dimensions. Remember that you can only add two matrices if they have the same dimensions—that is, the same number of rows as columns. So you got an “Error: Dimension Mismatch.” Hit ENTER to get out of this error and return to the main screen.
  10. Now try the same sequence without the + key: MATRX 1 MATRX 2 ENTER
    Figure 9
    Screenshot of a TI-83 graphing calculator displaying a matrix and the resulting product of multiplying matrices A & B.
    This instructs the calculator to multiply the two matrices. This is a legal multiplication—in fact, you may recognize it as the multiplication that we did earlier. The calculator displays the result that we found by hand: 123456789101112123456789101112 size 12{ left [ matrix { 1 {} # 2 {} # 3 {} ## 4 {} # 5 {} # 6 {} ## 7 {} # 8 {} # 9 {} ## "10" {} # "11" {} # "12"{} } right ]} {}104020503060104020503060 size 12{ left [ matrix { "10" {} # "40" {} ## "20" {} # "50" {} ## "30" {} # "60"{} } right ]} {} = 1403203207705001220680167014032032077050012206801670 size 12{ left [ matrix { "140" {} # "320" {} ## "320" {} # "770" {} ## "500" {} # "1220" {} ## "680" {} # "1670"{} } right ]} {}
  11. Enter a third matrix, matrix [C]= 34563456 size 12{ left [ matrix { 3 {} # 4 {} ## 5 {} # 6{} } right ]} {}. When you confirm that it is entered correctly, the screen should look like this:
    Figure 10
    Screenshot of a TI-83 graphing calculator displaying a 2x2 matrix.
    Now type MATRX 3 x-1 ENTER
    Figure 11
    Figure 11 (graphics11.png)
    This takes the inverse of matrix [C]. Note that the answer matches the inverse matrix that we found before.
  12. Type MATRX 3 x-1 MATRX 3 ENTER
    Figure 12
    Screenshot of a TI-83 graphing calculator .
    This instructs the calculator to multiply matrix [C]-1 times matrix [C]. The answer, of course, is the 2×2 identity matrix [I].

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