An augmented matrix that represents a system of linear equations (in variables x, y, and z) has been reduced using Gauss-Jordan elimination. Write the solution represented by the augmented matrix.
A) x = 0, y = 0, z = 0
B) x = -5x, y = -4y, z = -3z
C) x = -5, y = -3, z = -4
D) x = 5, y = 3, z = 4
E) x = -5, y = 0, z = 0

Question

An augmented matrix that represents a system of linear equations (in variables x, y, and z) has been reduced using Gauss-Jordan elimination. Write the solution represented by the augmented matrix. 
A) x = 0, y = 0, z = 0 
B) x = -5x, y = -4y, z = -3z 
C) x = -5, y = -3, z = -4 
D) x = 5, y = 3, z = 4 
E) x = -5, y = 0, z = 0

Quizplus · Accepted Answer

Since the augmented matrix has been reduced to a row echelon form or a reduced row echelon form using Gauss-Jordan elimination, the values of x, y, and z can be read off directly from the matrix. The values of the variables correspond to the entries in the last column of the matrix. In this case, the last column has the values [-5, -3, -4]. Therefore, the solution represented by the augmented matrix is x = -5, y = -3, and z = -4. Hence, the best choice is C.

An Augmented Matrix That Represents a System of Linear Equations