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

[2 3 –1] 1 2 – [2 3 –1] [–2 1 2] 1 2 – [–2 1 2] 2  3       23–1 –212 3  2       –12 = 2  2       94 –2 = MATRIX PRODUCT

Inverse of a Square Matrix

BASIC PROPERTIES OF MATRICES

BASIC PROPERTIES OF MATRICES Assume all products and sums are defined for the indicated matrices A, B, C, I, and

USING INVERSE METHODS TO SOLVE SYSTEMS OF EQUATIONS

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

Summary of Determinant Properties

Summary of Determinant Properties

Cramer's Rule for Three Equations and Three Variables X=y= z=