Calculator:
TI-83/84 plus.
Here is
a table of numbers that has three rows and four columns:
|
2.35 |
-4.3 |
7.65 |
0.01 |
|
0 |
-0.02 |
4.3 |
1.11 |
|
78.2 |
12 |
0 |
-6 |
In mathematical jargon a table of numbers that
has three rows and four columns is called a "three by four matrix." But you may call it a "three
by four table of numbers."
We are
going to use a very convenient notation, adopted by the TI-83/84. Each row of a table is included in square
brackets, and an extra pair of brackets is added around the whole table. In each row, numbers can be separated by
blanks or by commas
|
[[2.35 |
-4.3 |
7.65 |
0.01] |
|
[0 |
-0.02 |
4.3 |
1.11] |
|
[78.2 |
12 |
0 |
-6]] |
Now we
may also write the whole table in one line:
[[2.35, -4.3, 7.65, 0.01][0, -0.02, 4.3, 1.11][78.2, 12, 0, -6]]
The part
of mathematics that deals with tables of numbers is called linear algebra, or the algebra
of matrices. In arithmetic we
compute with numbers, and in "usual" algebra, variables range over
numbers. In linear algebra we compute
with whole tables of numbers, and variables range over tables of numbers. To avoid confusion we adopt the notation that
is used in the TI-83/84 calculator, so we will always encompass table-variables
in square brackets. Thus [X], [M], [A],
are variables ranging over matrices.
Task.
Use the matrix editor, 2nd
MATRIX EDIT 1,
to store the 3 by 4 matrix shown above in matrix-variable [A]. Leave the matrix editor by pressing 2nd
QUIT. Display the matrix on the home
screen by pressing, 2nd MATRIX 1 ENTER.
You will see only a part of the
table because it doesn't fit the screen.
[[2.35
4.3 7.6 ...
[0 -.02 4.3 ...
[78.2 0...
Use left
and right arrows, ←, → to see the rest of
it.
Now
execute:
Ans→[B]
(You
find [B] in 2nd MATRIX). Now you have two copies of the same table.
Execute;
[A]+[B] ENTER
[A]-[B] ENTER
10*[A] ENTER
What do
you see?
Use the
matrix editor 2nd MATRIX EDIT, to change just one number in matrix
[B]. Then execute again,
[A]-[B] ENTER
Arithmetic
of matrices (addition and subtraction).
You can add and subtract two matrices
providing that they have the same number of rows and the same number of
columns.
You can multiply a matrix by a
number.
Remark
about editing.
In order
to view or edit a matrix you may use the matrix editor. But there is another
way.
Execute:
2nd
RCL [A] ENTER
Matrix
[A] is dumped on the home screen. Now
you may use arrows to navigate it and edit it. After you have finished editing, put the cursor at the very end and
execute:
→[C] ENTER (store
the edited version in [C])
The
original [A] remains unchanged.