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- Determinants and Inverses of Matrices
The determinant of a 2 x 2 matrix
- Intro Lesson4:19
- Lesson: 11:33
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- Lesson: 41:32
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The determinant of a 2 x 2 matrix
In this lesson, we will learn how to find a determinant of a 2 x 2 matrix. To find the determinant, we multiply the top left entry and bottom right entry and subtract it with the product of the top right entry and bottom left entry. We will use these determinants later on in the course to show if a matrix is invertible. We will also use it to find inverses of 2 x 2 matrices.
Basic Concepts: Notation of matrices
Lessons
Let the matrix
, where a,b,c, and d are all numbers. We denote the determinant of X to be det(X). To find the determinant of a 2 x 2 matrix we compute the following:
det(X)=ad−bc

det(X)=ad−bc
- IntroductionThe determinant of a 2 x 2 matrix Overview
- 1.Finding the Determinant
You are given that. Find the determinant.
- 2.You are given that
. Find the determinant.
- 3.You are given that
. Find the determinant.
- 4.You are given that
. Find the determinant.
- 5.You are given that
. Find the determinant.
- 6.You are given that
. Find the determinant.
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40.
Determinants and Inverses of Matrices
40.1
The determinant of a 2 x 2 matrix
40.2
The determinant of a 3 x 3 matrix (General & Shortcut Method)
40.3
The inverse of a 2 x 2 matrix
40.4
The inverse of 3 x 3 matrices with matrix row operations
40.5
The inverse of 3 x 3 matrix with determinants and adjugate
40.6
2 x 2 invertible matrix
40.7
Solving linear systems using Cramer's Rule
40.8
Solving linear systems using 2 x 2 inverse matrices