# Vector operations on TI Calculators

**TI-89 SCALAR (DOT) PRODUCT OF VECTORS**

keystrokes:

<2^{nd}> then <5>MATH then nd <4> to select MATRIX from menu

scroll down menu to item L:Vector ops then press <ENTER>

scroll down menu to item 3:DotP( then press <ENTER>

In the command line enter, for example: [1,2,3],[4,5,6]) then press <ENTER>

note that the opening “(“ was already displayed

result display will be 32, which is the dot product of (1i + 2j + 3k) & (4i + 5j
+ 6k)

**TI-89 VECTOR (CROSS) PRODUCT OF VECTORS**

keystrokes:

<2^{nd}> then <5>MATH then <4> to select MATRIX from menu

scroll down menu to item L:Vector ops then press <ENTER>

scroll down menu to item 2:CrossP( then press <ENTER>

In the command line enter, for example: [1,2,3],[4,5,6]) then press <ENTER>

note that the opening “(“ was already displayed

resulting display will be [-3, 6, -3] which represents -3i + 6j - 3k,

the cross product of (1i + 2j + 3k) × (4i + 5j + 6k)

**Solving Simultaneous Equations With TI-82, TI-83, TI-83 Plus, and TI-83
Plus
Silver Edition Graphing Calculators**

(courtesy of Mr. Nabil Thalji)

Simultaneous equations can be solved quickly with several TI series graphing
calculators

using augmented matrices.

Procedure:

1. Press [2nd][x^{-1}] to access the matrix menu (for TI-82 and regular TI-83, this
is an

actual key and not the second function of the [x^{-1}] key).

2. Hit the right arrow button twice to scroll over to the EDIT tab, and select
the

matrix you want to edit (it does not matter which one you choose).

3. To edit the matrix, first enter the dimensions of the matrix. The dimensions

should be as follows: If you have two simultaneous equations, the dimensions

should be 2x3. If you have three equations, it should be 3x4. For 4, 4x5, and so

on.

4. Now begin entering the values into the matrix. Use one row per equation. Use

ONE column for each variable. The following is an example of how to enter the

values into the matrix properly:

Note that all the w coefficients are in the same column, and all the x
coefficients are in

the same column and so forth. Note that all constants are in the LAST column.
Also note

that each equation must be rewritten to the form Aw+Bx+Cy+Dz=C in order to be

translated directly into the matrix.

5. Hit [2nd][MODE], which is the QUIT function. This gets you out of the
matrix

editor. Hit [2nd][x-1] to return to the matrix menu and hit the right arrow key
once to

get to the MATH menu. Scroll down until you get to the function “rref(” (which
is the

12^{th} function in the list), and hit enter. Then return to the matrix menu again
([2nd][x-

1]), find the matrix you created (under the NAMES tab), and hit enter to select
it. This

puts the matrix within the rref( function so you should see something like this:

“rref([A]”. Hit enter again and you will get a reduced matrix that looks
something

like this:

(Note: the matrix may be too large to fit completely on
the screen, so use the right and

left arrow buttons to see the entire matrix. The above matrix is the solution of
the

example described in step 4.)

6. Recall which column represented which variable in your
initial augmented matrix.

The matrix in step 5 represents the following:

This method is very rapid once you have done it once or
twice, and doesn’t require

multiple matrices like Cramer’s rule. It is based on the reduction of an
augmented matrix

(shown in step 4) into what’s known as reduced row echelon form (shown in step
5).

Augmented matrices are terrible to reduce if you have to do it by hand, but
incredibly

simple if done on a calculator.