<< Chapter < Page | Chapter >> Page > |
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.
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
${x}^{\mathrm{\u20131}}$
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]
.)
NAMES
to
EDIT
. This signals that you want to create, or change, a matrix.
1
to indicate that you want to edit the
first matrix,
[A]
.4 ENTER 3 ENTER
to indicate that you want to create a 4x3 matrix. (4 rows, 3 columns.)
1 ENTER 2 ENTER 3 ENTER
4 ENTER 5 ENTER 6 ENTER7 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.
2nd Quit
to return to the main screen.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]
.
[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:
2nd MATRIX
instead of just
MATRX.
MATRX 1 + MATRX 2
This instructs the computer to add the two matrices. Now hit
ENTER
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.MATRX 1 MATRX 2 ENTER
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:
$\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\\ \text{10}& \text{11}& \text{12}\end{array}\right]$
$\left[\begin{array}{cc}\text{10}& \text{40}\\ \text{20}& \text{50}\\ \text{30}& \text{60}\end{array}\right]$ =
$\left[\begin{array}{cc}\text{140}& \text{320}\\ \text{320}& \text{770}\\ \text{500}& \text{1220}\\ \text{680}& \text{1670}\end{array}\right]$ MATRX 3 x-1 ENTER
This takes the
inverse of matrix [C]. Note that the answer matches the inverse matrix that we found before.MATRX 3 x-1 MATRX 3 ENTER
This instructs the calculator to multiply matrix [C]-1 times matrix [C]. The answer, of course, is the 2×2 identity matrix [I].Notification Switch
Would you like to follow the 'Advanced algebra ii: conceptual explanations' conversation and receive update notifications?