The determinant of a 2 x 2 matrix

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 matrix X = a b c d, where a,b,c,a, b, c, and dd are all numbers. We denote the determinant of XX to be det(X)(X). To find the determinant of a 2 x 2 matrix we compute the following:

det(X)=ad−bc(X)=ad-bc
  • Introduction
    The determinant of a 2 x 2 matrix Overview
  • 1.
    Finding the Determinant
    You are given that The determinant of a 2 x 2 matrix. Find the determinant.
  • 2.
    You are given that The determinant of a 2 x 2 matrix. Find the determinant.
  • 3.
    You are given that The determinant of a 2 x 2 matrix. Find the determinant.
  • 4.
    You are given that The determinant of a 2 x 2 matrix. Find the determinant.
  • 5.
    You are given that The determinant of a 2 x 2 matrix. Find the determinant.
  • 6.
    You are given that The determinant of a 2 x 2 matrix. Find the determinant.
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38.
Determinants and Inverses of Matrices
38.1
The determinant of a 2 x 2 matrix
38.2
The determinant of a 3 x 3 matrix (General & Shortcut Method)
38.3
The inverse of a 2 x 2 matrix
38.4
The inverse of 3 x 3 matrices with matrix row operations
38.5
The inverse of 3 x 3 matrix with determinants and adjugate
38.6
2 x 2 invertible matrix
38.7
Solving linear systems using Cramer's Rule
38.8
Solving linear systems using 2 x 2 inverse matrices
AU Year 10 Maths