Brief Instructions for Some Matrix
Operations Using the TI83/84 Series Calculator
NOTE: Follow instructions across from left
to right. Instructions may vary from TI83 to TI84, such as having to use
the 2^{nd} key to obtain Matrix on the TI83 Plus and TI84.


Entering and Editing a Matrix


Press MATRIX, right arrow to EDIT. Press Number 1 or highlight 1 and press ENTER. 
Matrix A is a 3x3. Press ENTER after each number. To save the matrix, press QUIT [2^{nd}
MODE]. 

Finding the Inverse and the Determinant of Matrix A 

To check the entries in Matrix A, press MATRIX,
number 1, and ENTER. 
To find 





To find the product of A inverse and A, press MATRIX, number 1, x^{1}, MATRIX, number 1, and ENTER. 
To find det(A), press MATRIX and the right arrow to highlight MATH. 





Press number 1, MATRIX, number 1, 



Adding and Multiplying Two Matrices 

Matrix D as shown to the right was stored in the TI83. 
To add matrix A and matrix D, press MATRIX, number 1,
+, MATRIX, number 4, and ENTER. 

To find the product of matrix A matrix D, press MATRIX,
number 1, MATRIX, number 4, and ENTER. 



Solve a System of Equations Using Gaussian Elimination and
GaussJordan Elimination Methods 

This is an augmented matrix used to solve a system of
three equations with variables x, y, and z. 
To solve by the Gaussian Elimination and BackSubstitution
method, use the ref( , rowechelon
form method. Press MATRIX, right arrow to get to MATH, and down arrow to ref(,
and ENTER 

With ref( on
the screen, return to the matrix menu to obtain Matrix A and press ENTER 
The third column of ref
( [ A ] ) is 2.75, 0.2, and 0.2. From Row 3, we get z = 0.2. Use this value to
backsubstitute into Row 2 and get y = 0. Substitute the y and zvalues into Row 1 to get x = 2.8. So our solution is (2.8, 0, 0.2). 

To solve by the GaussianJordan Elimination method, use
the rref(
, reduced rowechelon form method. Press MATRIX, right arrow to get to
MATH, and down arrow to rref(, and ENTER 
With rref( on the screen, return to the matrix menu to obtain Matrix A and press ENTER 
The third column of rref
( [ A ] ) is 2.8, 0, and 0.2. The matrix is in reduced rowechelon form. Row 1 indicates that x = 2.8. Row 2 indicates that y = 0. Row 3 yields z = 0.2. So our solution is (2.8, 0, 0.2). 

Solve a System of Equations Using Matrices: X = A^{1}B 

Enter the coefficients of the variables as Matrix A and the constants as Matrix B as shown on the right.

Press Matrix,
number 1, and x^{1} to get [A]^{1}.
Press Matrix,
number 2 to get [B]. Once [A]^{1}[B]
is on screen, press Enter to get
the answer. So our solution is (2.8,
0, 0.2). 