Coefficient matrix

Definition

A coefficient matrix is a rectangular array that contains only the coefficients of the variables in a system of linear equations. It is used to facilitate methods such as Gaussian Elimination and finding matrix inverses.

5 Must Know Facts For Your Next Test

1. The coefficient matrix does not include constants from the equations, only coefficients of variables.
2. Each row in the coefficient matrix corresponds to an equation in the system.
3. Gaussian Elimination can be performed directly on the augmented matrix, which includes both the coefficient matrix and the constants.
4. For a system with n equations and m variables, the coefficient matrix will be an n x m matrix.
5. The determinant of the coefficient matrix must be non-zero for there to be a unique solution using inverses.

Review Questions

• What elements are included in a coefficient matrix?
• How does Gaussian Elimination utilize the coefficient matrix?
• Why is it important to know whether the determinant of a coefficient matrix is zero or non-zero?

Related terms

Augmented Matrix:

An augmented matrix includes both the coefficients of the variables and the constants from each equation in a system of linear equations.

Determinant:

A scalar value that can be computed from a square matrix and determines whether a unique solution exists for a system of linear equations.

$Gaussian\ Elimination$: $A\ method\ for\ solving\ systems\ of\ linear\ equations\ by\ transforming\ the\ augmented\ matrix\ into\ reduced\ row-echelon form.$