TI-83: Simple 3 equation 3 variable, but with no solution, non-parallel.

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, but two parallel planes.
The next example page covers a Simple 3 equation 3 variable situation, with fractional coefficients, but integer answers.

WARNING: The TI-83 and TI-83 Plus are almost identical in terms of the material presented here. The major difference is the labels that are on certain keys. The TI-83 has a

key, whereas on the TI-83 Plus requires 2 keys to achieve the same result, namely, the

key. The text below will be done from the perspective of the TI-83. That is, all reference to the MATRIX key will be demonstrated via the

key. If the user has a TI-83 Plus then the key strokes should be

. To save some space, and to ignore this difference, the numeric keys (the gray ones) have been changed in some places to show the key face, as in

. In addition, the

key may be shown as

and the

key may be shown as

, again to save space.

The problem we will use on this page is 22x + 32y - 7z = 234
9x - 5y - 30z = -49
13x + 37y + 23z = 482 Note that the detailed explanations of the earlier pages will not be repeated here. Instead, the explanations for the calculator images will make reference to the general steps that have been taken.

Figure 1 Open the matrix menu and move to the editor. We will use [A] for this problem.

Figure 2 Enter the coefficients and the constants into the matrix.
Verify the values.

Figure 3 Mave to display the first column so that we can verify values in that column.

Figure 4 Exit the matrix editor and return to the main screen Figure 4 shows the remnants of the previous example. We want to recall and execute again the command shown in Figure 4.

Figure 5 We will recall the desired command, rref([A]). After recalling the command, we pressed to have the calculator perform the command. The result is the matrix shown at the bottom of the screen.
As was the case in the previous example, the resulting matrix does not have the diagonal 1's form. And, in the same way that we looked at the previous example, it is clear that there is no possible solution to the matrix given in Figure 5. Therefore, this matrix indicates that there is no solution to the original system of linear equations.

We return to the original problem,

22x + 32y - 7z = 234
9x - 5y - 30z = -49
13x + 37y + 23z = 482 Unlike the case shown in the previous example, there are no parallel planes in this system of linear equalities. Rather, each pair of equations represent planes that intersect. However, there is no point where all three planes intersect. The following diagram is meant to illustrate htree such planes.

We can see that the each pair of planes intersect. However the lines of intersection, d, e, and f, are parallel. Thus, there is no point where all three planes intersect.

Figure 1	Open the matrix menu and move to the editor. We will use [A] for this problem.
Figure 2	Enter the coefficients and the constants into the matrix. Verify the values.
Figure 3	Mave to display the first column so that we can verify values in that column.
Figure 4	Exit the matrix editor and return to the main screen Figure 4 shows the remnants of the previous example. We want to recall and execute again the command shown in Figure 4.
Figure 5	We will recall the desired command, rref([A]). After recalling the command, we pressed to have the calculator perform the command. The result is the matrix shown at the bottom of the screen. As was the case in the previous example, the resulting matrix does not have the diagonal 1's form. And, in the same way that we looked at the previous example, it is clear that there is no possible solution to the matrix given in Figure 5. Therefore, this matrix indicates that there is no solution to the original system of linear equations.