guass elimination method
10x-2y+3z=23
2x+10y-5z=-33
3x-4y+10z=41
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Answer:
augmented matrix.
For example, consider the following 2 × 2system of equations.
3x + 4y = 7
4x − 2y = 5
We can write this system as an augmented matrix (please note that a more common formatting for augmented matrices has a solid vertical line running through the matrix, rather than a line on each row):
[
3
4
|
7
4
−
2
|
5
]
[34|74−2|5]
We can also write a matrix containing just the coefficients. This is called the
coefficient matrix.
[
3
4
4
−
2
]
[344−2]
A three-by-three system of equations such as
3x − y − z = 0
x + y = 5
2x − 3z = 2
has a coefficient matrix
⎡
⎢
⎣
3
−
1
−
1
1
1
0
2
0
−
3
⎤
⎥
⎦
[3−1−111020−3]
and is represented by the augmented matrix
⎡
⎢
⎣
3
−
1
−
1
∣
0
1
1
0
∣
5
2
0
−
3
∣
2
⎤
⎥
⎦
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