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

Solution

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 \(\boxed{\begin{bmatrix} 5 & 2 & 9 \ 6 & -6 & 4 \end{bmatrix}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/RRgMg7l717/

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