1. 4-6 3x3 Matrices, Determinants, & Inverses

2. Objectives
Evaluating Determinants of 3 x 3 Matrices Using Inverse 3 x 3 Matrices

3. Using a Graphing Calculator to find the Determinant
Enter matrix T into your graphing calculator. Use the matrix submenus to evaluate the determinant of the matrix.
–2 –
T =
The determinant of the matrix is –65.

4. Verifying Inverses
Determine whether the matrices are multiplicative inverses.
a. C = , D = =
Since CD I, C and D are not multiplicative inverses. = /

5. Continued (continued) b. A = , B = 0 0 1 0 1 0 1 0 –1 1 0 1 0 1 0 –1 = –1
Since AB = I, A and B are multiplicative inverses.

6. Solving a Matrix Equation –1 8 –2
Solve the equation.
X =
Let A =
Find A–1.
X = – –2 –1 8 –2
Use the equation X = A–1C.
Multiply.
X = –2 –4 3

7. Real World Example Use the alphabet table and the encoding matrix.
0.25 – –1
matrix K =
a. Find the decoding matrix K–1.
K–1 = Use a graphing calculator.
– –0.75
– –1.25

8. Continued (continued) 11.25 16.75 24.5 5.75 17 5.5 1.5 –12 15 –
b. Decode Zero indicates a space holder. =
– –0.75
– –1.25 –
Use the
decoding
matrix
from
part (a).
Multiply.
The numbers correspond to the letters NEAT CODE.

9. Homework
Pg # 5, 6, 8, 9, 10 ,11