Example
:
Find the line of intersection of the planes 3
x
+
2
y
+
z
= 
1
and 2
x

y
+
4
z
=
5.
§
1.1 and
§
1.2
1.24
GaussJordan Elimination
Definition
(1)
Write the augmented matrix of the system of linear equations.
(2)
Use elementary row operations to reduce the augmented matrix
to reduced row echelon form.
(3)
If the resulting system is consistent, solve for the leading
variables in terms of any remaining free variables.
Example
:
Find the line of intersection of the planes 3
x
+
2
y
+
z
= 
1
and 2
x

y
+
4
z
=
5.
[
A

b
]
=
•
3
2
1

1
2

1
4
5
‚
§
1.1 and
§
1.2
1.24
GaussJordan Elimination
Definition
(1)
Write the augmented matrix of the system of linear equations.
(2)
Use elementary row operations to reduce the augmented matrix
to reduced row echelon form.
(3)
If the resulting system is consistent, solve for the leading
variables in terms of any remaining free variables.
Example
:
Find the line of intersection of the planes 3
x
+
2
y
+
z
= 
1
and 2
x

y
+
4
z
=
5.
[
A

b
]
=
•
3
2
1

1
2

1
4
5
‚
R
2
=
3
R
2

2
R
1
→
§
1.1 and
§
1.2
1.24
GaussJordan Elimination
Definition
(1)
Write the augmented matrix of the system of linear equations.
(2)
Use elementary row operations to reduce the augmented matrix
to reduced row echelon form.
(3)
If the resulting system is consistent, solve for the leading
variables in terms of any remaining free variables.
Example
:
Find the line of intersection of the planes 3
x
+
2
y
+
z
= 
1
and 2
x

y
+
4
z
=
5.
[
A

b
]
=
•
3
2
1

1
2

1
4
5
‚
R
2
=
3
R
2

2
R
1
→
•
3
2
1

1
0

7
10
17
‚
§
1.1 and
§
1.2
1.24
GaussJordan Elimination
Definition
(1)
Write the augmented matrix of the system of linear equations.
(2)
Use elementary row operations to reduce the augmented matrix
to reduced row echelon form.
(3)
If the resulting system is consistent, solve for the leading
variables in terms of any remaining free variables.
Example
:
Find the line of intersection of the planes 3
x
+
2
y
+
z
= 
1
and 2
x

y
+
4
z
=
5.
[
A

b
]
=
•
3
2
1

1
2

1
4
5
‚
R
2
=
3
R
2

2
R
1
→
•
3
2
1

1
0

7
10
17
‚
R
2
:
=
R
2
/
7
→
R
1
:
=
R
1
/
3
§
1.1 and
§
1.2
1.24
GaussJordan Elimination
Definition
(1)
Write the augmented matrix of the system of linear equations.
(2)
Use elementary row operations to reduce the augmented matrix
to reduced row echelon form.
(3)
If the resulting system is consistent, solve for the leading
variables in terms of any remaining free variables.
Example
:
Find the line of intersection of the planes 3
x
+
2
y
+
z
= 
1
and 2
x

y
+
4
z
=
5.
[
A

b
]
=
•
3
2
1

1
2

1
4
5
‚
R
2
=
3
R
2

2
R
1
→
•
3
2
1

1
0

7
10
17
‚
R
2
:
=
R
2
/
7
→
R
1
:
=
R
1
/
3
•
1
2
/
3
1
/
3

1
/
3
0
1

10
/
7

17
/
7
‚
§
1.1 and
§
1.2
1.24
GaussJordan Elimination
Definition
(1)
Write the augmented matrix of the system of linear equations.
(2)
Use elementary row operations to reduce the augmented matrix
to reduced row echelon form.
(3)
If the resulting system is consistent, solve for the leading
variables in terms of any remaining free variables.
Example
:
Find the line of intersection of the planes 3
x
+
2
y
+
z
= 
1
and 2
x

y
+
4
z
=
5.