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| + | *Hey, did you know this is your user page? Every time you leave your signature and someone clicks on the link, this is where it goes. Just saying because you might want to move these theories to the [[MA351 | MA 351 Course Page ]] and leave more room here for your own personal stuff, and feel free to delete my comments either way. [[User:Jhunsber|Josh Hunsberger]] | ||
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[['''Purdue University''']] | [['''Purdue University''']] | ||
[[MATH351: Linear Algebra and its applications]] | [[MATH351: Linear Algebra and its applications]] | ||
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| + | == ''RREF (Reduced Row Echelon Form)'' == | ||
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A matrix is in RREF form if it satisfies all of the following conditions: | A matrix is in RREF form if it satisfies all of the following conditions: | ||
a. If a row has nonzero entries, then the first nonzero entry is 1, called the leading 1 (or pivot) in this row. | a. If a row has nonzero entries, then the first nonzero entry is 1, called the leading 1 (or pivot) in this row. | ||
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b. If a column contains a leading 1, then all the other entries in that column are 0. | b. If a column contains a leading 1, then all the other entries in that column are 0. | ||
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c. If a row contains leading 1, then each row above it contains a leading 1 further to the left. | c. If a row contains leading 1, then each row above it contains a leading 1 further to the left. | ||
Condition c implies that rows of 0's, if any, appear at the bottom of the matrix. | Condition c implies that rows of 0's, if any, appear at the bottom of the matrix. | ||
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| + | == '''Definition: Rank''' == | ||
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| + | The rank of matrix A is the number of leading 1's in rref A | ||
Latest revision as of 07:29, 22 February 2010
- Hey, did you know this is your user page? Every time you leave your signature and someone clicks on the link, this is where it goes. Just saying because you might want to move these theories to the MA 351 Course Page and leave more room here for your own personal stuff, and feel free to delete my comments either way. Josh Hunsberger
MATH351: Linear Algebra and its applications
RREF (Reduced Row Echelon Form)
A matrix is in RREF form if it satisfies all of the following conditions:
a. If a row has nonzero entries, then the first nonzero entry is 1, called the leading 1 (or pivot) in this row.
b. If a column contains a leading 1, then all the other entries in that column are 0.
c. If a row contains leading 1, then each row above it contains a leading 1 further to the left.
Condition c implies that rows of 0's, if any, appear at the bottom of the matrix.
Definition: Rank
The rank of matrix A is the number of leading 1's in rref A
