# Matrices

## Cramer’s rule

On this post we explain what Cramer’s rule is and, in addition, you will find examples and exercises of systems of equations solved by Cramer’s rule. Cramer’s rule formula Cramer’s rule is a formula used to solve systems of linear equations using determinants. Let’s see how to use the Cramer’s rule: Given a system of …

## Eigenvalues and eigenvectors of a matrix

On this post we explain what the eigenvalues and the eigenvectors of a matrix are. You will also find examples of how to compute the eigenvalues and the eigenvectors of a matrix, and finally, you have problems with solutions solved step by step to practice. What are the eigenvalues and the eigenvectors of a matrix? …

## Jacobian matrix and determinant

On this post you will find what the Jacobian matrix is and how to calculate it. In addition, you have several solved Jacobian matrix exercises to practice. You will also see why the determinant of the Jacobian matrix, the Jacobian, is so important. Finally, we explain the applications that this type of matrix has. What …

## Hessian matrix

On this post we explain what the Hessian matrix is and how to calculate it (with examples). Also, you will find several solved exercises so that you can practice. In addition, you will see all the applications of the Hessian matrix. And finally, we will show you what the bordered Hessian matrix is. What is …

## Involutory matrix

On this post we explain what an involutory matrix is. We also show you examples of 2×2, 3×3 and 4×4 involutory matrices. And finally, you will find the formula of an involutory matrix and all the properties of this type of matrices. What is an involutory matrix? The definition of involutory matrix is as follows: …

## Gaussian elimination method

On this post you will learn what the Gaussian elimination method is and how to solve a system of equations by the Gaussian elimination method. What is the Gaussian elimination method? The Gaussian elimination method, also called row reduction method, is an algorithm used to solve a system of linear equations with a matrix. The …

## Inverse of a matrix

We explain what the inverse of a matrix is and how to find it. You will learn the formulas to calculate the inverse of a 2×2 matrix and the inverse of a 3×3 matrix. Also, you will see several solved examples. And finally, we explain the properties of the inverse matrix. What is the inverse …