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Reduced Echelon Form & Row Reduction Algorithm
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Video Outline:
0:00 Introduction
0:21 Definition of a nonzero row
0:27 Definition of the leading entry of a row
0:38 Reduced Echelon Form Definition
1:03 Echelon Form Definition
1:21 Examples of Echelon & Reduced Echelon Matrices
3:52 Discussion - Why do we care about (reduced) echelon matrices?
4:33 Row Reduction Algorithm (RRA) / Gaussian Elimination
4:49 Step 1 of RRA
5:00 pivot column/pivot position definition
5:21 Step 2 of RRA
5:49 Definition of a pivot
6:00 Why is it called a pivot?
7:23 Step 3 of RRA
8:05 Step 4 of RRA
9:44 Step 5 of RRA
11:08 Steps 1-4 of RRA give echelon matrix (not unique)
11:45 Step 5 gives reduced echelon matrix (unique)
12:21 Definition of (Reduced) Echelon Form of a matrix
12:42 Pivot Position Definition
0:00 Introduction
0:21 Definition of a nonzero row
0:27 Definition of the leading entry of a row
0:38 Reduced Echelon Form Definition
1:03 Echelon Form Definition
1:21 Examples of Echelon & Reduced Echelon Matrices
3:52 Discussion - Why do we care about (reduced) echelon matrices?
4:33 Row Reduction Algorithm (RRA) / Gaussian Elimination
4:49 Step 1 of RRA
5:00 pivot column/pivot position definition
5:21 Step 2 of RRA
5:49 Definition of a pivot
6:00 Why is it called a pivot?
7:23 Step 3 of RRA
8:05 Step 4 of RRA
9:44 Step 5 of RRA
11:08 Steps 1-4 of RRA give echelon matrix (not unique)
11:45 Step 5 gives reduced echelon matrix (unique)
12:21 Definition of (Reduced) Echelon Form of a matrix
12:42 Pivot Position Definition
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