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. $\left[ \begin{array} { c c c : c }
1 & 0 & 0 & - 3 \
0 & 1 & 0 & - 6 \
0 & 0 & 1 & 1
\end{array} \right]$
A)x = -3, y = -6, z = 1
B)x = 3, y = 6, z = -1
C)x = 0, y = 0, z = 0
D)x = -3x, y = y, z = -6z
E)x = -3, 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. $\left[ \begin{array} { c c c : c } 
1 & 0 & 0 & - 3 \
0 & 1 & 0 & - 6 \
0 & 0 & 1 & 1
\end{array} \right]$
A)x = -3, y = -6, z = 1
B)x = 3, y = 6, z = -1
C)x = 0, y = 0, z = 0
D)x = -3x, y = y, z = -6z
E)x = -3, y = 0, z = 0

Quizplus · Accepted Answer

The augmented matrix is in reduced row echelon form, with each row representing an equation for one of the variables x, y, and z. The solution is directly read off as x = -3, y = -6, z = 1.

An Augmented Matrix That Represents a System of Linear Equations [100−3010−60011]\left[ \begin{array} { c c c : c } 1 & 0 & 0 & - 3 \\0 & 1 & 0 & - 6 \\0 & 0 & 1 & 1\end{array} \right]​100​010​001​−3−61​​

An Augmented Matrix That Represents a System of Linear Equations $\left[ \begin{array} { c c c : c } 1 & 0 & 0 & - 3 \\0 & 1 & 0 & - 6 \\0 & 0 & 1 & 1\end{array} \right]$