TI - 83 MATRIX MANIPULATIONS

1. Entering a matrix into the calculator: To enter a matrix into the calculator first press: MATRIX > > (The " > " symbol indicates that you are to press the right arrow key. " > > " indicates that you are to press the right arrow key twice, etc. The arrow keys are located in the upper right portion of the calculator below the calculator viewing window.)

This moved the cursor on the display screen to EDIT.

Now select a matrix name from the choices of [A], [B], [C],�, [J] available under NAMES on the display screen. To select the matrix name [C] for example, move the lower cursor on the display screen to [C] and press: ENTER This will display : MATRIX [C] 1 X 1 [0 ]

You are now ready to enter the dimension of the matrix and the elements of the matrix. To enter the elements of the 4 X 5 matrix given by under the matrix name [C] for example, given below:

First press 4 ENTER 5 ENTER to enter the dimension of the matrix. Notice that the cursor has moved to the position of the element of the first row and first column of the matrix.

To enter the elements of the first row, press: 1 ENTER (-) 2 ENTER 3 ENTER (-) 4 ENTER 40 ENTER

Repeat the process for the elements of the other rows. We have now entered the given matrix under the matrix name [C]. Quit by pressing: 2nd MODE

Exercise: Enter the following matrices into your calculator under the assigned names:

2. Matrix Operations: From Part 1 above, matrices are stored in the memory of the calculator under the matrix names [A], [B], [C], [D], [E], and [F]. We will do some simple matrix computations with these matrices.

(a) Multiply a Matrix by a constant:

To do (-2)[A]: Press (-) 2 * MATRIX ENTER ENTER Write the displayed matrix

(-2)[A] =

(b) Add two matrices together:

To do [A] + [F]: Press MATRIX ENTER + MATRIX 6 (5 times) ENTER ENTER Also do [A] - [F] and write the displayed matrices

[A] + [F] =

[A] - [F] =

( c) Multiply two matrices:

To do [A] x [D]: Press MATRIX ENTER * MATRIX V (down arrow) (3 times) ENTER ENTER Write the matrix displayed and state the dimension of the product.

Also do [D] x [A], [A] x [B], [B] x [E], [F] x [D], [E] x [B], and [D] x [F] if possible. If not possible, say why.

[D] x [A] =	[F] x [D] =
[A] x [B] =	[E] x [B] =
[B] x [E] =	[D] x [F] =

(d) Finding the transpose ( ) of a matrix:

To do :

Press MATRIX ENTER MATRIX > (right arrow) V (down arrow) ENTER ENTER

Write the matrix displayed :

(e) Finding the inverse () of a matrix :

To do :

Press MATRIX V V V (i.e., down arrow 3 times) Then press ENTER ENTER

Write the matrix displayed.

Find . You should have got an error. Why ?

Find D x , and x D.

D x =

x D =

(f) Putting a matrix into row - echelon form:

To obtain the row - echelon form of the real matrix A: Press MATRIX > (right arrow) V (down arrow) ( 10 times) ENTER MATRIX ENTER ) ENTER

Write the matrix displayed

(g) Putting a matrix into reduced row - eschelon form :

To obtain the reduced row - echelon form of the real matrix C: Press MATRIX > (right arrow) V (down arrow 11 times) ENTER MATRIX V V (down arrow 2 times) ENTER ) ENTER

Write the matrix displayed

(h) Interchanging (swapping) rows on a matrix:

To do the row swap on D: