3: Determinants — Read — Invisible Network

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3.1: Basic Techniques
Let \(A\) be a square matrix. The determinant of \(A\), denoted by \( \det (A) \), is an important number that gives us some very useful information about the matrix. We will explore the determinant throughout this section and chapter.
- 3.1E: Exercises for Section 3.1
3.2: Properties of Determinants
There are many important properties of determinants. Since many of these properties involve the row operations discussed in Chapter 1, we recall that definition now. We will now consider the effect of row operations on the determinant of a matrix. In future sections, we will see that using the following properties can greatly assist in finding determinants. This section will use the theorems as motivation to provide various examples of the usefulness of the properties.
- 3.2E: Exercises for Section 3.2
3.3: Application of the Determinant to Inverses; Cramer's Rule
The determinant of a matrix also provides a way to find the inverse of a matrix.
- 3.3E: Exercises for Section 3.3
3.4: Determinants and Geometry
In this section we give a geometric interpretation of determinants, in terms of volumes. This will shed light on the reason behind three of the four defining properties of the determinant. It is also a crucial ingredient in the change-of-variables formula in multivariable calculus.
- 3.4E: Exercises for Section 3.4

This page titled 3: Determinants was last modified on Tue, 30 Jul 2024 00:24:50 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Doli Bambhania, De Anza College.

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