Brief Instructions for Some Matrix Operations Using the TI-83/84 Series Calculator

 

NOTE: Follow instructions across from left to right. Instructions may vary from TI-83 to TI-84, such as having to use the 2nd key to obtain Matrix on the TI-83 Plus and TI-84.

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 [2nd 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
A inverse, press MATRIX, number 1,
x
-1, and ENTER.

 

 

 

 

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,
close ), and ENTER.
det([A]) = -1

 

 

Adding and Multiplying Two Matrices

Matrix D as shown to the right was stored in the TI-83.

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 Gauss-Jordan 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 Back-Substitution method, use the ref( , row-echelon 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 back-substitute into Row 2 and get y = 0.

 

Substitute the y- and z-values into Row 1 to get x = 2.8. So our solution is (2.8, 0, 0.2).

To solve by the Gaussian-Jordan Elimination method, use the rref( , reduced row-echelon 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 row-echelon 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-1B

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).