Math 2331
Linear Algebra
Section 3.2
Solving Ax = 0
Matrices in Row Reduced Echelon Form
An mxn augmented matrix is in
rowreduced echelon form
if it satisfies the following
conditions:
1.
Each row consisting entirely of zeros lies below any other row having nonzero entries.
2.
The first nonzero entry in each row is 1 (called a
leading 1
). (the PIVOTS)
3.
In any two successive (nonzero) rows, the leading 1 in the lower row lies to the right
of the leading 1 in the upper row.
4.
If a column contains a leading 1 (pivot), then the other entries in that column are
zeros.
Pivot Column:
A column in the row reduced echelon form of
coefficient matrix is a
pivot column if one of the entries in the column is a 1 and the other entries are zeros.
Example:
Determine which of the following matrices are in rowreduced form.
If a
matrix is not in rowreduced form, state which condition is violated.
a.
1000
0100
0012
⎛⎞
⎜
⎜
⎜⎟
⎝⎠
⎟
⎟
e
.
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 Spring '08
 Staff
 Linear Algebra, Algebra, Matrices, Vector Space, Row Reduced Echelon

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