1. Copyright © 2001 by the McGraw-Hill Companies, Inc. Barnett/Ziegler/Byleen Precalculus: Functions & Graphs, 5 th Edition Chapter Nine Matrices & Determinants

2. [2 3 –1] 1 2 –1 3 0 2 [2 3 –1] [–2 1 2] 1 2 –1 3 0 2 [–2 1 2] 2  3       23–1 –212 3  2       13 20 –12 = 2  2       94 –2 = MATRIX PRODUCT 9-1-94

3. Inverse of a Square Matrix 9-2-95

4. BASIC PROPERTIES OF MATRICES 9-3-96-1

5. BASIC PROPERTIES OF MATRICES Assume all products and sums are defined for the indicated matrices A, B, C, I, and 0. 9-3-96-2

6. USING INVERSE METHODS TO SOLVE SYSTEMS OF EQUATIONS 9-3-97

7. DEFINITION 2 The value of a determinant of order 3 is the sum of three products obtained by multiplying each element of any one row (or each element of any one column) by its cofactor. Theorem 1 Expansion along the first row Expansion along the first column Value of a Third-Order Determinant 9-4-98

8. Summary of Determinant Properties 9-5-99-1

9. Summary of Determinant Properties 9-5-99-2

10. Cramer's Rule for Three Equations and Three Variables X=y= z= 9-6-100