Write the system of equations represented by the augmented matrix shown.

• A. $x+2y+3z=5;5y+4z=1;4x+7y=12$
• B. $x+2y+3x=5;5x+4y=1;4x+7y=12$
• C. $x+2y+3x=5;5y+4z=1;4y+7z=12$
• D. $x+2y+3x=-5;5y+4z=-1;4x+7y=-12$

Answer: (A)

Verified step by step guidance

1. Understand that an augmented matrix represents a system of linear equations. Each row corresponds to an equation, and each column corresponds to the coefficients of the variables in the system.
2. Identify the variables in the system. Typically, the variables are x, y, and z, corresponding to the columns of the matrix before the augmentation line.
3. Translate the first row of the matrix [1, 2, 3 | 5] into an equation. The coefficients 1, 2, and 3 correspond to the variables x, y, and z, respectively, resulting in the equation: x + 2y + 3z = 5.
4. Translate the second row of the matrix [0, 5, 4 | 1] into an equation. The coefficients 0, 5, and 4 correspond to the variables x, y, and z, respectively, resulting in the equation: 5y + 4z = 1.
5. Translate the third row of the matrix [4, 7, 0 | 12] into an equation. The coefficients 4, 7, and 0 correspond to the variables x, y, and z, respectively, resulting in the equation: 4x + 7y = 12.