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MATH 115
STEP BY STEP ROW REDUCTION
1. Write out the augmented matrix for the given system of equations.

2
x
3
+ 7
x
5
= 12
2
x
1
+ 4
x
2

10
x
3
+ 6
x
4
+ 12
x
5
= 28
2
x
1
+ 4
x
2

5
x
3
+ 6
x
4

5
x
5
=

1
→
2. Locate the leftmost column of the augmented matrix that is not all zeros.
3. Interchange the top row with another row (if necessary) to put a nonzero entry at the top of this
column.
4. If the entry that is now at the top of this column is
a
6
= 1, multiply the ﬁrst row by
1
a
to get a pivot.
5. Add suitable multiples of the top row to the entries below so that all entries below the pivot become
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Unformatted text preview: 0’s. 6. Cover the top row in the matrix and start again with Step 1 on the matrix that remains. Continue until entire matrix is in REF. → → → 7. Beginning with the last nonzero row and working up, add multiples of each row to the rows above to introduce 0’s above the leading 1’s. → →...
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This note was uploaded on 01/13/2011 for the course MATH math 136 taught by Professor Brown during the Spring '08 term at Waterloo.
 Spring '08
 brown
 Math, Equations

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