Minors and Cofactors
The matrix created after eliminating the row and column of the matrix in which that specific element lies is defined as the minor of the matrix.
The minor of the element a12 is M12 – [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]=\left[\begin{matrix}a_{21}&a_{23}\\a_{31}&a_{33}\\\end{matrix}\right] [/Tex]
The cofactor of an element in matrix A is produced by multiplying the element’s minor Mij by (-1)i+j . Cij is the symbol for an element’s cofactor. If the minor of a matrix is Mij , then the cofactor of the element would be Cij = (-1)i+j Mij. The cofactor matrix is the matrix created by the cofactors of the matrix’s components.
Cofactor Matrix : [Tex]\left[\begin{matrix}C_{11}&C_{12}&C_{13}\\C_{21}&C_{22}&C_{23}\\C_{31}&C_{32}&C_{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?