List all of the 3×5 RREFs with three leading ones. If such matrices are augmented with a bar between columns 4 and 5, what are the possible geometries of their solution sets?
List all of the 3×5 RREFs with three leading ones. If such matrices are augmented with a bar between columns 4 and 5, what are the possible geometries of their solution sets?
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.CM: Cumulative Review
Problem 17CM: Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]
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Question
List all of the 3×5 RREFs with three leading ones. If such matrices are
augmented with a bar between columns 4 and 5, what are the possible
geometries of their solution sets?
Expert Solution
Step 1
In this solution we will discuss and list all the row reduced echelon forms with three leading ones.
We know that a matrix is said to row reduced echelon form if:
- It is in echelon form. That is the matrix in a shape which is resulting of the Gaussian elimination.
- The leading entry in each non zero row is .
- Each column containing the leading has other entry zero.
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