Chapter 1

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Last updated 7:35 AM on 4/25/26
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8 Terms

1
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The PIVOT of a row in a matrix is…

the leftmost non-zero entry in that row

2
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A matrix is in ROW ECHELON FORM if…

  1. all rows containing only zeros are at the bottom

  2. the pivot of each non-zero row is in the column to the right of the pivot above it

3
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A matrix is in REDUCED ROW ECHELON FORM if…

  1. in RE form

  2. the pivot of each non-zero row is 1

  3. each pivot is the only non-zero entry in its column

4
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We say that xi is a BASIC VARIABLE for the system if…

the ith column of RREF(C) has a pivot

5
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We say that xi is a FREE VARIABLE for the system if…

the ith column of RREF(C) does not have a pivot

6
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The system is inconsistent if and only if…

the last column of RREF(A) has a pivot

7
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The system has exactly one solution if and only if…

the last column of RREF(A) does not have a pivot, and every column of RREF(C) has a pivot

8
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The system has infinitely many solution if and only if…

the last column of RREF(A) does not have a pivot, and RREF(C) has a column without a pivot