 # 4-6 3x3 Matrices, Determinants, & Inverses

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4-6 3x3 Matrices, Determinants, & Inverses

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

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.

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

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.

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

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

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.

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