We are looking for the values of the variables, s, t, u, v,w, x, and y, that will make all seven equations true. To do this we will create a matrix that represents the equations presented above. In particular, we want the calculator to hold the matrix
2 | -7 | 3 | 5 | -7 | 11 | 8 | 114 |
5 | 7 | -1 | 9 | -6 | 3 | -5 | -11 |
13 | 11 | 8 | 7 | 4 | 2 | 1 | -25 |
12 | 1 | 6 | 5 | 9 | 3 | 11 | -37 |
1 | -4 | 7 | -3 | 9 | -2 | 6 | 4 |
4 | 1 | -6 | -3 | 8 | -7 | -4 | -91 |
-7 | -2 | 5 | 1 | 9 | 3 | -4 | -50 |
There are two ways to enter a matrix into the calculator. First, you can use the [ and ] characters to type the matrix directly into the calcualtor. That method was demonstrated in the 3 variable, 3 equation page. Second, you can use the Matrix Editor. That is the method presented here, in Figures 1 through 6. The other Figures on this page are used to demonstrate how the calculator produces the reduced row echelon form of the given matrix.
![]() | Open the matrix menu with the ![]() ![]() ![]() ![]() |
![]() | Before we edit the numbers that are in the matix, the calculator allows us
to change the size of the matrix. [A] has 3 rows and 4 columns from its earlier definition.
We need to make [A] have seven rows and eight columns. Therefore,
press ![]() ![]() ![]() ![]() |
![]() | Notice in Figure 3 that the matrix [A] appears in its expanded form.
By default, the
new cells of the matrix have been assigned the value 0.
The highlight is on the item at row 1 column 1. The old value for that cell was 5, as shown here in the
matrix and in Figure 2. The new value will be 2. We have pressed the
![]() ![]() |
![]() | Figure 4 shows the rightmost 3 columns of elements in the matrix after all 56 values have been entered. |
![]() | Use the ![]() |
![]() | Use the ![]() After we have verified the contents of [A], we exit the
matrix editor via the |
![]() | The main screen of the calculator used here still shaows the previous command
used, rref([A]), and the results of that command. In fact, that was the
command used in the previous example page,
s3_3x3o.htm. Since then we have changed the size and the contents
of [A]. Nonetheless, we want to construct that same command. We can do that
by recalling the last command by pressing
![]() ![]() |
![]() | The command has been recalled. Press
![]() |
![]() | THe reduced row echelon form of the matrix appears in Figure 9.
Unfortunately, we can only see the leftmost 7 columns. They have the expected 1's
down the main diagonal with 0's above and below.
The final column is off the screen. However, we can use the
![]() |
![]() | Now we can see the eighth column. We could translate this matrix
back to the equation format to produce:
0s + 1t + 0u + 0v + 0w + 0x + 0y = -7 0s + 0t + 1u + 0v + 0w + 0x + 0y = 8 0s + 0t + 0u + 1v + 0w + 0x + 0y = -6 0s + 0t + 0u + 0v + 1w + 0x + 0y = -9 0s + 0t + 0u + 0v + 0w + 1x + 0y = 2 0s + 0t + 0u + 0v + 0w + 0x + 1y = -3 |
The main page for solving systems of linear equations on the TI-83 and TI-83 Plus.
The previous example page covers a Simple 3 equation 3 variable situation
with other variables.
The next example page covers a 3 equation 3 variable
situation, where some variables may be missing.
©Roger M. Palay
Saline, MI 48176
November, 2010