Coefficient and augmented matrices

Prerequisites

Cartesian Coordinates Show

Gradient of a straight line Show

Equation of a straight line Show

Linear Equations Show

Matrices Show

Systems of linear equations Show

Coefficient and augmented matrices

Introduction

  • Given a system of linear equations: a system of linear equations
  • It can be very time consuming to write this out.
  • Instead, we can omit the variables and write the coefficients as a matrix: the coefficients of the system as a matrix
  • This is called a coefficient matrix
  • We can add an extra column to this matrix to also store the values on the right side of the equals sign: the coefficient matrix with an extra column for the values
  • This is called an augmented matrix.
  • Augmented matrices are easier and clearer to work with than fully explicit systems of linear equations.

LaTeX

\left\[\begin{matrix}
1 & 1 & 1 \\
1 & 2 & 3 \\
3 & 6 & -1
\end{matrix}
\,\,\right|
\left.\begin{matrix}
5 \\
3 \\
1
\end{matrix}\right]