I'm struggling to understand why there is a 1 at the bottom of the row (first and third example of the matrix in row echelon form) when the definition it states that for it to be in row echelon form it must have the bottom row entirely consisting of zeros. Please explain with as much simplicity and conciseness as possible, breaking it down bit by bit. Many thanks.
I'm struggling to understand why there is a 1 at the bottom of the row (first and third example of the matrix in row echelon form) when the definition it states that for it to be in row echelon form it must have the bottom row entirely consisting of zeros. Please explain with as much simplicity and conciseness as possible, breaking it down bit by bit. Many thanks.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I'm struggling to understand why there is a 1 at the bottom of the row (first and third example of the matrix in row echelon form) when the definition it states that for it to be in row echelon form it must have the bottom row entirely consisting of zeros. Please explain with as much simplicity and conciseness as possible, breaking it down bit by bit.
Many thanks.
Transcribed Image Text:Definition 1.8. A matrix is said to be in row echelon form if it satisfies the following
three conditions:
(i) All zero rows (consisting entirely of zeros) are at the bottom.
(ii) The first non-zero entry from the left in each nonzero row is a 1, called the leading
1 for that row.
(iii) Each leading 1 is to the right of all leading 1's in the rows above it.
dition i
Transcribed Image Text:Example 1.9. Matrices in row echelon form:
1
4 2
1 3 1 0
0
1 3
0013
0000
0 0 1,
Matrices in reduced row echelon
2 0 1
0 1 2
0 0 0
1
0
0
0
1
form:
"
/0 1 2)
(13)
2)
0 0 1
150 2
0 3
(3) ()
001 -1
0 1 2
0 0 0 0
000
2
The variables corresponding to the leading 1's of the augmented matrix in row ech-
elon form will be referred to as the leading variables, the remaining ones as the free
variables.
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