The least squares problem is to obtain a vector that the distance of the value of the given linear map at that vector from another given vector is minimized. More specifically, let \(A\) be an \(m \times n\) real matrix and \(b\) a vector in \(\mathbb{R}^m\). The least squares problem is to find a suitable…

# Tag: systems of linear equations

## Gaussian elimination

Gaussian elimination is the name of an algorithm which uses a sequence of elementary row operations to solve a system of linear equations. In the post on systems of linear equations, we introduced systems of linear equations, the matrix of coefficients, and the augmented matrix. Here we first introduce the back-substitution method to solve special…

## Systems of linear equations

A system of linear equations is a set of linear equations with the same variables (unknowns). Systems of linear equations are used in many areas of science and engineering, such as data science and analysis. In this post, we discuss systems of linear equations and how to solve them with some examples. First we discuss…