AUGMENTED MATRIX

Augmented Matrix

Definition Of Augmented Matrix

Augmented matrix is a coefficient matrix that has an extra column containing the constant terms and this extra column is separated by a vertical line.

Examples of Augmented Matrix

3x - 7y = 16
5x + 8y = 9
The augmented matrix for the given system of equations is:
example of Augmented Matrix

Video Examples: Introduction to Augmented Matrices

Solved Example on Augmented Matrix

Ques: Which of the following represents the system of equations of the augmented matrix?

example of Augmented Matrix

Choices:

A. 8x - y = 2, 6x + y = 2
B. 8x + y = 2, 6x - y = - 2
C. 8x - y = - 2, 6x + y = - 2
D. 8x - y = 2, 6x + y = - 2
Correct Answer: D

Solution:

Step 1: example of Augmented Matrix
Step 2: Multiplying the two matrices
Step 3: By the definition of equal matrices 8x - y = 2, 6x + y = - 2

Quick Summary

Represents a system of linear equations.
Used to solve systems of equations using row operations (Gaussian elimination).
The last column represents the constants on the right-hand side of the equations.

\[ N/A (representation, not a formula) \]

🍎 Teacher Insights

Emphasize the connection between the augmented matrix and the original system of equations. Use visual aids to demonstrate row operations. Provide ample practice problems.

🎓 Prerequisites

System of Equations
Matrices
Coefficient Matrix

Check Your Knowledge

Q1: Which augmented matrix represents the system: x + y = 3, x - y = 1?

[ [1, 1, 3], [1, -1, 1] ] [ [1, 1, 1], [1, -1, 3] ] [ [1, 3, 1], [1, 1, -1] ] [ [3, 1, 1], [1, 1, -1] ]

Frequently Asked Questions

Q: How do I convert a system of equations into an augmented matrix?
A: Each row represents an equation. The coefficients of the variables are entered in order, and the constants are entered in the last column, separated by a vertical line (often implied).

Q: What does the last column of the augmented matrix represent?
A: The constants on the right-hand side of the equations.