An augmented matrix that represents a system of linear equations (in variables x, y, z and w if applicable) has been reduced using Gauss-Jordan elimination.Find the solution represented by the augmented matrix. $\left[ \begin{array} { c c c c }
1&0&0&\vdots& -3 \
0&1&0&\vdots& -9 \
0 & 0 & 1 &\vdots&3\
\end{array} \right]$
A) (-3, 9, 3)
B)(3, -9, 3)
C)(-3, -9, 3)
D)(-3, -9, -3)
E)(-3, 3, -9)

Question

An augmented matrix that represents a system of linear equations (in variables x, y, z and w if applicable) has been reduced using Gauss-Jordan elimination.Find the solution represented by the augmented matrix.   $\left[ \begin{array} { c c c c } 
1&0&0&\vdots& -3 \
0&1&0&\vdots& -9 \
0 & 0 & 1 &\vdots&3\
\end{array} \right]$  
A) (-3, 9, 3)
B)(3, -9, 3)
C)(-3, -9, 3)
D)(-3, -9, -3)
E)(-3, 3, -9)

Quizplus · Accepted Answer

The augmented matrix is in reduced row echelon form, indicating that the system of equations has a unique solution. Each row represents an equation for one of the variables (x, y, z) in that order, with the solutions being the constants on the right side of the augmented matrix. Thus, the solution is x = -3, y = -9, z = 3, which matches choice C.

An Augmented Matrix That Represents a System of Linear Equations [100⋮−3010⋮−9001⋮3]\left[ \begin{array} { c c c c } 1&0&0&\vdots& -3 \\0&1&0&\vdots& -9 \\0 & 0 & 1 &\vdots&3\\\end{array} \right]​100​010​001​⋮⋮⋮​−3−93​​

An Augmented Matrix That Represents a System of Linear Equations $\left[ \begin{array} { c c c c } 1&0&0&\vdots& -3 \\0&1&0&\vdots& -9 \\0 & 0 & 1 &\vdots&3\\\end{array} \right]$