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
.
1 0
0
1
−
