Figure 01 ![]() |
Open the PROGRAM menu by pressing the
![]() |
Figure 02 ![]() |
Use the ![]() ![]() |
Figure 03 ![]() |
Figure 03 shows the command needed to actually run the progrm.
We just need to press ![]() |
Figure 04 ![]() |
The program starts with a request for the value of the first key. The program tries to convey the meaning of the key value: we have one Wasted digit or symbol (explained later), 5 Seed value digits for the random number generator, 3 Range digits, and 2 Start digits. The program uses these to determine the lowest allowd value in the matrix (SS) and the range of values allowed (RRR).Thus, the highest value in the matrices will be LL+RRR. The Wasted value is ignored, unless it is a negative sign, in which case the LL value is taken to be negative. |
Figure 05 ![]() |
We respond, in Figure 05, with the value
322597401810 , which means that the lowest value in the generated matrices is
10 and the highest is 28 .
You might check the ten matrices shown above to verify that those limits
were in fact used.
Press ![]() |
Figure 06 ![]() |
The program prompts for the second key. This time the
program tries to help us by giving us the hint
EEDDCCBBAA RCRCRCRCRC to tell us that the two leftmost of the ten digits will specify the number of rows and columns in matrix E, the next two digits will specify the number of rows and columns in matrix D, and so on. The response that we enter, 2424434343 , specifies that
E is a 2x4, D is a 2x4, C is a 4x3, B is a 4x3,
and A is a 4x3. Press ![]() |
Figure 07 ![]() |
The program starts to do its work. It creates and displays matrix A
and waits for us to press ![]() |
Figure 08 ![]() |
It creates and displays matrix B
and waits for us to press ![]() |
Figure 09 ![]() |
It creates and displays matrix C
and waits for us to press ![]() |
Figure 10 ![]() |
It creates and displays matrix D
and waits for us to press ![]() ![]() |
Figure 11 ![]() |
Now the program asks for the row and column sizes
of the last five matrices, J, I, H, G, and F.
Our response of 3434342424
specifies that
J is a 3x4, I is a 3x4, H is a 3x4, G is a 2x4,
and F is a 2x4. Press ![]() |
Figure 12 ![]() |
It creates and displays matrix F
and waits for us to press ![]() ![]() |
Figure 13 ![]() |
It creates and displays matrix H
and waits for us to press ![]() |
Figure 14 ![]() |
It creates and displays matrix I
and waits for us to press ![]() |
Figure 15 ![]() |
It creates and displays matrix J and the program is done. |
Figure 16 ![]() |
We use the ![]() ![]() |
Figure 17 ![]() |
To get to Figure 17; we use the ![]() We press ![]() |
Figure 18 ![]() |
To do matrix addition we just need to form the command using the +
sign. We can accomplish this via the ![]() |
Figure 19 ![]() |
In this example we want to add [J] to [H} so we need to get the
name [H]to end our command.
We cannot type that name. Rather, we need to return to the matrix menu,
via ![]() ![]() ![]() |
Figure 20 ![]() |
Press ![]() |
Figure 21 ![]() |
With the command completed we just need to press
![]() |
Figure 22 ![]() |
The result is shown in Figure 22. Here we see that
It should be clear that the algorith used to add two matrices is
to form a new matrix, of the same dimension,
where the elements of the new matrix
are just the sum of the corresponding elements of the original
two matrices. In this example, the 32 in the
first row, first column of the answer is just the sum of the
21 and 11 that are in the same position
in [J] and [H], respectively.
The requirement for adding two matrices is that they have to have the same dimensions, i.e., they must have an identical number of rows and an identical number of columns. Our example worked because the two original matrices each had 3 rows and 4 columns. |
Figure 23 ![]() |
One important property of addition that we learned when dealing with numeric
values is that the opertion of addition for numbers is
commutative, which means that
x + y = y + x .
Considering that to add two matrices we just add the respective component elements of the
matrices we should expect that the operation of addition for matrices is commutative.
Giving an example does not prove that this is true, but Figure 23 does show that
[H]+[J] gives the same result as we had for [J]+[H].
|
Figure 24 ![]() |
Another numeric property of addition is that the operation is associative.
That means that for any numbers, x, y, and z
it is always true that
x + (y + ) = (x + y) + z .
We can give an example of this for matrices. In Figure 24 we find [H]+([I]+[J]).
|
Figure 25 ![]() |
Then in Figure 25 we find ([H]+([I])+[J]. The result is the same. Again, this is not a shock given that when we add matrices we are just adding corresponding elements from the matrices involved. This is not a proof. Rather it is an illustration the addition of matrices is associative. |
Figure 26 ![]() |
What happens on the calculator if we try to add matrices that do not have
the same dimensions? We can try this via
[A]+[H], trying to add a 4x3 and a 3x4 matrices. Figure 26 shows the command.
Press ![]() |
Figure 27 ![]() |
The calculator detects the error and reports it
as shown in Figure 27.
We can press Press ![]() |
Figure 28 ![]() |
Note that the alculator marked the previous command as an Error. |
Figure 29 ![]() |
We saw that we could not add [A] and [H], but we can add [A] and [C]. The result is shown in Figure 29. |