Advanced Engineering Mathematics, 7th Edition

8.4 Determinants

INTRODUCTION

Suppose A is an n × n matrix. Associated with A is a number called the determinant of A and is denoted by det A. Symbolically, we distinguish a matrix A from the determinant of A by replacing the parentheses by vertical bars:

A determinant of an n × n matrix is said to be a determinant of order n. We begin by defining the determinants of 1 × 1, 2 × 2, and 3 × 3 matrices.

A Definition

For a 1 × 1 matrix A = (a), we have det A = |a| = a. For example, if A = (−5), then det A = |−5| = −5. In this case the vertical ...