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### Row Operations and an Augmented Matrix

```
Date: 07/26/99 at 15:52:41
From: Shelley Tomberlin
Subject: Linear systems of equations

it, the more confused I become. These were the instructions I was
given:

Solve the following linear system of equations by using row operations
on the augmented matrix of the system. Show ALL checks and write the
final answer in ordered notation. Our professor prefers that ALL other
numbers be zeroed out except the numbers in the diagonal position.

a -  b      - d + e = -10
2a -  b - 3c + d - e =   0
2b      - d + e =  -1
-3a      +  c     + e =   5
a -  b - 4c + d - e =   4

Thanks.
```

```
Date: 07/27/99 at 05:46:18
From: Doctor Anthony
Subject: Re: Linear systems of equations

The augmented matrix is

[ 1   -1    0   -1    1 | -10]  r1
| 2   -1   -3    1   -1 |   0|  r2
| 0    2    0   -1    1 |  -1|  r3
|-3    0    1    0    1 |   5|  r4
[ 1   -1   -4    1   -1 |   4]  r5

r2 = r2 + r4 + r5

[ 1   -1    0   -1    1 | -10]  r1
| 0   -2   -6    2   -1 |   9|  r2
| 0    2    0   -1    1 |  -1]  r3
|-3    0    1    0    1 |   5|  r4
[ 1   -1   -4    1   -1 |   4]  r5

r4 = r4 + 3.r5

[1   -1     0   -1    1 | -10]  r1
|0   -2    -6    2   -1 |   9|  r2
|0    2     0   -1    1 |  -1]  r3
|0   -3   -11    3   -2 |  17|  r4
[1   -1    -4    1   -1 |   4]  r5

r5 = r5 - r1

[1   -1     0   -1    1 | -10]  r1
|0   -2    -6    2   -1 |   9|  r2
|0    2     0   -1    1 |  -1]  r3
|0   -3   -11    3   -2 |  17|  r4
[0    0    -4    2   -2 |  14]  r5

and continuing with these row operations we end up with

[1   0   0   0   0 | -3]  r1
|0   1   0   0   0 |  2|  r2
|0   0   1   0   0 | -1]  r3
|0   0   0   1   0 |  2|  r4
[0   0   0   0   1 | -3]  r5

and so  a = -3,  b = 2,  c = -1,  d = 2,  e = -3

- Doctor Anthony, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Linear Algebra

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