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### Using an Augmented Matrix

```
Date: 11/21/1999 at 16:31:02
From: Katie
Subject: Augmented matrices

I'm really stuck on how to solve augmented matrices. I understand how
you solve for 1 in cell 11 and I understand you have to add row 1 and
row 2 to get a new row 2, but I don't understand what to multiply when
you are adding the two equations. The problem is this:

x + 3y +  z = 3
x + 5y + 5z = 1
2x + 6y + 3z = 8

so the matrix becomes

[1 3 1 | 3]
[1 5 5 | 1]
[2 6 3 | 8]

So then you add row 1 [1 3 1 | 3] to row 2 [1 5 5 | 1], but what does
row 1 get multiplied by?
```

```
Date: 11/21/1999 at 18:30:17
From: Doctor Anthony
Subject: Re: Augmented matrices

[ 1   3   1   |   3 ]     r1
[ 1   5   5   |   1 ]     r2
[ 2   6   3   |   8 ]     r3

r2 = r2-r1

[ 1   3   1   |   3 ]     r1
[ 0   2   4   |  -2 ]     r2
[ 2   6   3   |   8 ]     r3

r3 = r3-2r1

[ 1   3   1   |   3 ]     r1
[ 0   2   4   |  -2 ]     r2
[ 0   0   1   |   2 ]     r3

r2 = r2/2

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

At this stage we can see

z = 2

y + 4 = -1   so   y = -5

x - 15 + 2 = 3    so   x = 16

The solution set is x = 16, y = -5, z = 2

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

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