Adjoint of a matrix
Let A=[aij] be an n-dimensional square matrix. A matrix A’s adjoint is the transpose of A’s cofactor matrix. It is symbolized by the letter adj A. Adjoint matrices are sometimes known as adjugate matrices. The adjoint of a square matrix A = [aij]n x n is defined as the transpose of the matrix [Aij]n x n, where Aij is the cofactor of the element aij.
[Tex]Let A = \left[\begin{matrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\\\end{matrix}\right] [/Tex]
Adjoint of A=Transpose of [Tex]\left[\begin{matrix}A_{11}&A_{12}&A_{13}\\A_{21}&A_{22}&A_{23}\\A_{31}&A_{32}&A_{33}\\\end{matrix}\right] [/Tex] = [Tex]\left[\begin{matrix}A_{11}&A_{21}&A_{31}\\A_{12}&A_{22}&A_{32}\\A_{13}&A_{23}&A_{33}\\\end{matrix}\right][/Tex]
How to Solve a System of Equations using Inverse of Matrices?
How to Solve a System of Equations Using Inverse of Matrices? In mathematics, a matrix is an array of numbers arranged in a rectangular pattern and separated into rows and columns. They’re commonly depicted by enclosing all of the integers within square brackets.
In this article, we will discuss how to solve a system of equations using the inverse of matrices in detail.
Table of Content
- Determinant
- Minors and Cofactors
- Adjoint of a matrix
- Inverse of a matrix
- Application of Matrices and Determinants
- Representing linear systems with matrix equations
- Solving equations with inverse matrices
- Problems on How to Solve a System of Equations using Inverse of Matrices?
- Practice Problems on How to Solve a System of Equations using Inverse of Matrices?