Use the matrix features on a graphing calculator to express the augmented matrix in reduced row echelon form. $$\left[ \begin{array} { c c c | c }
- 3 & 1 & - 3 & - 5 \
- 1 & 2 & 5 & - 11 \
5 & 2 & 4 & 2
\end{array} \right]$$

A)
$\left[ \begin{array} { l l l | c }
1 & 0 & 0 & 2 \
0 & 1 & 0 & - 2 \
0 & 0 & 1 & - 1
\end{array} \right]$
B)

$\left[ \begin{array} { c c c | c }
1 & 0 & 0 & 2 \
0 & 1 & 0 & 1 \
0 & 0 & 1 & - 2
\end{array} \right]$

C)
$\left[ \begin{array} { c c c | c } 1 & 0 & 0 & 2 \ 0 & 1 & 0 & - 2 \ 0 & 0 & 1 & 0 \end{array} \right]$

D)
$\left[ \begin{array} { c c c | c } 1 & 0 & 0 & 2 \ 0 & 1 & 0 & 1 \ 0 & 0 & 1 & - 2 \end{array} \right] ;$ inconsistent system

Question

Use the matrix features on a graphing calculator to express the augmented matrix in reduced row echelon form. $$\left[ \begin{array} { c c c | c } 
- 3 & 1 & - 3 & - 5 \
- 1 & 2 & 5 & - 11 \
5 & 2 & 4 & 2
\end{array} \right]$$

A)
$\left[ \begin{array} { l l l | c } 
1 & 0 & 0 & 2 \
0 & 1 & 0 & - 2 \
0 & 0 & 1 & - 1
\end{array} \right]$
B)

$\left[ \begin{array} { c c c | c } 
1 & 0 & 0 & 2 \
0 & 1 & 0 & 1 \
0 & 0 & 1 & - 2
\end{array} \right]$

C) 
$\left[ \begin{array} { c c c | c } 1 & 0 & 0 & 2 \ 0 & 1 & 0 & - 2 \ 0 & 0 & 1 & 0 \end{array} \right]$

D) 
$\left[ \begin{array} { c c c | c } 1 & 0 & 0 & 2 \ 0 & 1 & 0 & 1 \ 0 & 0 & 1 & - 2 \end{array} \right] ;$ inconsistent system

Quizplus · Accepted Answer

Using a graphing calculator to perform matrix row operations to achieve reduced row echelon form (RREF) of the given augmented matrix results in the matrix where each variable (represented by columns 1 through 3) has been isolated, leading to a unique solution for each variable. This is represented by the matrix in option A, where the system of equations has been solved to yield $x = 2$, $y = -2$, and $z = -1$.

Use the Matrix Features on a Graphing Calculator to Express [−31−3−5−125−115242]\left[ \begin{array} { c c c | c } - 3 & 1 & - 3 & - 5 \\- 1 & 2 & 5 & - 11 \\5 & 2 & 4 & 2\end{array} \right]​−3−15​122​−354​−5−112​​

Use the Matrix Features on a Graphing Calculator to Express $\left[ \begin{array} { c c c | c } - 3 & 1 & - 3 & - 5 \\- 1 & 2 & 5 & - 11 \\5 & 2 & 4 & 2\end{array} \right]$