HP 10413 Datasheet download pdf (Page 195)

195

The result is a triangle with corners at (1,1),

(2,1) and (1,3), along with its image after

reflection in the x axis.

We can now matrix M1 so that it contains

another matrix. For example:

To see the effect of this new matrix, simply

return to the HOME view, the previous

calculation and press ENTER. The new image

will be stored into matrix M3. If you now return

to the PLOT view the image will not appear to

have changed as the aplet does not realize the

matrix has changed but pressing PLOT again

will force a re-draw of the new image.

The power of this aplet as an investigative tool is that you can now continue

to matrix M1, repeat the HOME calculation, and re-plot to see

immediately the change in the image.

The degree of guidance which should be given to a class will obviously

depend on their level of ability. You might choose simply to suggest that they

confine their investigations initially to placing numbers only on the diagonals.

It is a good idea to challenge them to record their matrices on the board as

they discovered them. A highly able class will find nearly all relevant matrices

within 20 to 30 minutes.

So… how does this aplet work?

The formulas in the SYMB view form the key to

the process by allowing the calculator to fetch

values from the matrices, with the values

fetched being determined by the settings in the

PLOT SETUP view. For example, as T runs

from 1 to 4 in steps of 1 the (X1,Y1) values

plotted become (M2(1,1),M2(2,1)), (M2(1,2),M2(2,2)),

(M2(1,3),M2(2,3)) and (M2(1,4),M2(2,4)). If we now

substitute the actual values from matrix M2 then these points become (1,1),

(2,1), (3,1) and (1,1), which give the shape when plotted. The repetition of the

first point is to ensure that the line forming the triangle is closed by

connecting back to its starting point. Obviously X2 and Y2 perform the same

function with matrix M3.

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HP 10413 Datasheet Page 195