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. Identify the augmented matrix provided: [[1, 2, 3 | 5], [0, 5, 4 | 1], [4, 7, 0 | 12]].
2. Understand that each row of the matrix corresponds to an equation in the system of equations. The numbers before the vertical line represent the coefficients of the variables x, y, and z, and the number after the line represents the constant term.
3. Translate the first row of the matrix into an equation: 1x + 2y + 3z = 5.
4. Translate the second row of the matrix into an equation: 0x + 5y + 4z = 1. Since the coefficient of x is 0, x does not appear in this equation.
5. Translate the third row of the matrix into an equation: 4x + 7y + 0z = 12. Since the coefficient of z is 0, z does not appear in this equation.