Use row operations on the augmented matrix to solve the given system of linear equations.
A) , ,
B) , ,
C) , ,
D) , ,
E) , ,

Question

Use row operations on the augmented matrix to solve the given system of linear equations. ​  ​
A) , , 
B) , , 
C) , , 
D) , , 
E) , ,

Quizplus · Accepted Answer

Performing row operations on the augmented matrix, we can reduce it to row echelon form:

\begin{bmatrix}
1 & -2 & 1 & 2 \
0 & 1 & -2 & 3 \
0 & 0 & 0 & 1 \
\end{bmatrix}

This corresponds to the system:

\begin{align*}
x_1 - 2x_2 + x_3 &= 2 \
x_2 - 2x_3 &= 3 \
0 &= 1 \
\end{align*}

The last equation indicates that there is no solution to the system.

The only choice that includes a row of zeros in the reduced form is option C, which indicates that the system has no solution.

Use Row Operations on the Augmented Matrix to Solve the Given