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Leto [7]
3 years ago
8

Write the coefficient matrix and the augmented matrix of the given system of linear equations.

Mathematics
1 answer:
Alex787 [66]3 years ago
6 0

Answer:

The coefficient matrix is represented by \vec A = \left[\begin{array}{ccc}7&6\\2&-8\end{array}\right].

The augmented matrix is represented by \left(\vec A|\vec B\right) = \left[\begin{array}{ccc}7&6&6\\2&-8&4\end{array}\right].

Step-by-step explanation:

From Linear Algebra we know that a system of n linear equations with n variables can be represented as a matrix product:

\vec {A}\cdot \vec {x} = \vec{B}

Where:

\vec{A} - Coefficient matrix, a n \times n matrix.

\vec{x} - Variable matrix, a n \times 1 matrix.

\vec{B} - Equivalence matrix, a n \times 1 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]

The coefficient matrix is represented by \vec A = \left[\begin{array}{ccc}7&6\\2&-8\end{array}\right].

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]

The augmented matrix is represented by \left(\vec A|\vec B\right) = \left[\begin{array}{ccc}7&6&6\\2&-8&4\end{array}\right].

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