Copyright © 1999 by the McGraw-Hill Companies, Inc. Barnett/Ziegler/Byleen College Algebra, 6 th Edition Chapter Seven 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

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=