Problem

Write the coefficient matrix and the augmented matrix of the given system of linear equations.
\[
\begin{array}{l}
5 x_{1}+2 x_{2}=9 \\
6 x_{1}-6 x_{2}=4
\end{array}
\]

What is the coefficient matrix?
\[
\left[\begin{array}{c}
5 \square \\
\square \square
\end{array}\right]
\]

What is the augmented matrix?
\[
\left[\begin{array}{ll|l}
5 & \square & \square \\
\square & \square & \square
\end{array}\right] \text { (Do not simplify.) }
\]

Answer

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Answer

Final Answer: The coefficient matrix is \(\boxed{\begin{bmatrix} 5 & 2 \ 6 & -6 \end{bmatrix}}\) and the augmented matrix is \(\boxed{\begin{bmatrix} 5 & 2 & 9 \ 6 & -6 & 4 \end{bmatrix}}\).

Steps

Step 1 :Write the coefficient matrix and the augmented matrix of the given system of linear equations.

Step 2 :The coefficient matrix is formed by the coefficients of the variables in the system of equations. In this case, the coefficient matrix is \(\begin{bmatrix} 5 & 2 \ 6 & -6 \end{bmatrix}\).

Step 3 :The augmented matrix is formed by extending the coefficient matrix to include the constants on the right side of the equations. In this case, the augmented matrix is \(\begin{bmatrix} 5 & 2 & 9 \ 6 & -6 & 4 \end{bmatrix}\).

Step 4 :Final Answer: The coefficient matrix is \(\boxed{\begin{bmatrix} 5 & 2 \ 6 & -6 \end{bmatrix}}\) and the augmented matrix is \(\boxed{\begin{bmatrix} 5 & 2 & 9 \ 6 & -6 & 4 \end{bmatrix}}\).

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