Answer:
The coefficient matrix is represented by
.
The augmented matrix is represented by
.
Step-by-step explanation:
From Linear Algebra we know that a system of
linear equations with
variables can be represented as a matrix product:

Where:
- Coefficient matrix, a
matrix.
- Variable matrix, a
matrix.
- Equivalence matrix, a
matrix.
Then, the given system is represented as:
![\left[\begin{array}{ccc}7&6\\2&-8\end{array}\right]\left[\begin{array}{ccc}x_{1}\\x_{2}\end{array}\right] = \left[\begin{array}{ccc}6\\4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%266%5C%5C2%26-8%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx_%7B1%7D%5C%5Cx_%7B2%7D%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%5C%5C4%5Cend%7Barray%7D%5Cright%5D)
The coefficient matrix is represented by
.
The augmented matrix consist in the union of the coefficient and equivalence matrices. That is:
![\left(\vec A|\vec B\right) = \left[\begin{array}{ccc}7&6&6\\2&-8&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%28%5Cvec%20A%7C%5Cvec%20B%5Cright%29%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%266%266%5C%5C2%26-8%264%5Cend%7Barray%7D%5Cright%5D)
The augmented matrix is represented by
.