# Row reduction and echelon forms

##### Intros
###### Lessons
1. Row Reduction and Echelon Form Overview:
2. Echelon Matrix vs. Reduced Echelon Matrix
• 3 properties for echelon form
• Addition 2 properties for reduced echelon form
• What is the difference between them?
3. Pivot Position and Pivot Column
• pivot position = leading entry
• pivot column = column of pivot position
4. The Row Reduction Algorithm
• The 5 steps of the algorithm
• Making sure it is in reduced echelon form
5. Solutions of Linear Systems
• Reduced echelon form of augmented matrix
• Basic variables and free variables
• Writing out the solutions
##### Examples
###### Lessons
1. Difference between Echelon Form and Reduced Echelon Form
Label whether the following matrices are in echelon form or reduced echelon form:
2. Learning the Row Reduction Algorithm
Row reduce the matrices to reduced echelon form. Circle the pivot positions in the final and original matrix, and list the pivot columns from the original matrix in part b:
3. Finding the General Solution of a Matrix
Find the general solution of the following matrices:
4. Linear Systems with Unknown Constants
Choose values of a and b where the system has infinitely many solutions, and no solutions:
1. $x_1+ax_2=4$
$2x_1+4x_2=b$
2. $3x_1-x_2=6$
$x_1+ax_2=b$