TI-83: Simple 7 equation 7 variable

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

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.

Figure 1	Open the matrix menu with the key. Use to move the highlight to the EDIT command at the top of the screen. The calculator used here has two previously defined matrices, [A] and [C]. For this problem we will re-use matrix [A].Note that matrix [A] is already selected. Therefore, press to move to Figure 2.
Figure 2	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 to make this change and move to Figure 3.
Figure 3	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 key to enter that new value. It appears at the bottom of the screen. To get the calculator to accept that value, press .
Figure 4	Figure 4 shows the rightmost 3 columns of elements in the matrix after all 56 values have been entered.
Figure 5	Use the key to move the highlight to the left in order to shift the display so that we can see other columns. The highlight in Figure 5 is on the item in row 7 column 3. Thus, the screen in Figure 5 displays columns 3, 4, and 5.
Figure 6	Use the key to move the highlight to the left in order to shift the display so that we can see remaining columns. The highlight in Figure 6 is on the item in row 7 column 1. Thus, the screen in Figure 6 displays columns 1, 2, and 3. After we have verified the contents of [A], we exit the matrix editor via the key sequence. This will return the calculator to the main screen.
Figure 7	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 result is shown in Figure 8.
Figure 8	The command has been recalled. Press to perform the command.
Figure 9	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 key to shift the display to the right.
Figure 10	Now we can see the eighth column. We could translate this matrix back to the equation format to produce: 1s + 0t + 0u + 0v + 0w + 0x + 0y =  5 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 which simplifies to s=5, t=–7, u=8, v=– 6, w=– 9, x=2, and y=– 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.