Augmented matrix

Definition

An augmented matrix is a matrix derived from a system of linear equations, which includes the coefficients and constants of the equations. It is used to simplify solving systems using methods like Gaussian elimination.

5 Must Know Facts For Your Next Test

1. It represents both the coefficients and constants of a system of linear equations.
2. The vertical line or partition in an augmented matrix separates the coefficients from the constants.
3. It is essential for performing Gaussian elimination to solve systems of equations.
4. An augmented matrix can be row-reduced to find solutions to a system of linear equations.
5. Equivalent systems have equivalent augmented matrices after row operations.

Review Questions

• What does an augmented matrix represent in a system of linear equations?
• How is an augmented matrix used in Gaussian elimination?
• What does the vertical line in an augmented matrix signify?

Related terms

Gaussian Elimination: A method for solving systems of linear equations by transforming the system's augmented matrix into reduced row echelon form.

Row Operations: Operations including row swapping, scaling rows, and adding/subtracting rows that are used to manipulate matrices during methods like Gaussian elimination.

Reduced Row Echelon Form (RREF): A form of a matrix where each leading entry is 1, all elements above and below leading entries are zero, and each leading entry is to the right of the leading entry in the previous row.