Use the given row transformation to change the matrix as indicated.
-$\left[ \begin{array} { r r r } 3 & 5 & 12 \ 1 & 3 & 2 \ 2 & - 3 & 3 \end{array} \right] ; - 2$ times row 2 added to row 3
A)
$\left[ \begin{array} { r r r } 3 & 5 & 12 \ 1 & 3 & 2 \ 0 & - 6 & 1 \end{array} \right]$

B)
$\left[ \begin{array} { r r r } 3 & 5 & 12 \ 1 & 3 & 2 \ 0 & - 9 & - 1 \end{array} \right]$
C)
$\left[\begin{array}{rrr}
3 & 5 & 12 \
1 & 3 & 2 \
4 & 3 & 7
\end{array}\right]$

D)
$$\left[ \begin{array} { r r r }
1 & - 1 & 8 \
1 & 3 & 2 \
2 & - 3 & 3
\end{array} \right]$$

Question

Use the given row transformation to change the matrix as indicated.
-$\left[ \begin{array} { r r r } 3 & 5 & 12 \ 1 & 3 & 2 \ 2 & - 3 & 3 \end{array} \right] ; - 2$ times row 2 added to row 3
A)
$\left[ \begin{array} { r r r } 3 & 5 & 12 \ 1 & 3 & 2 \ 0 & - 6 & 1 \end{array} \right]$

B)
$\left[ \begin{array} { r r r } 3 & 5 & 12 \ 1 & 3 & 2 \ 0 & - 9 & - 1 \end{array} \right]$
C)
$\left[\begin{array}{rrr}
3 & 5 & 12 \
1 & 3 & 2 \
4 & 3 & 7
\end{array}\right]$

D)
$$\left[ \begin{array} { r r r } 
1 & - 1 & 8 \
1 & 3 & 2 \
2 & - 3 & 3
\end{array} \right]$$

Quizplus · Accepted Answer

To perform the row operation "-2 times row 2 added to row 3", we multiply each element in row 2 by -2 and add the result to the corresponding element in row 3. For row 2, the elements are (1, 3, 2). Multiplying by -2 gives (-2, -6, -4). Adding these to row 3's elements (2, -3, 3) gives (0, -9, -1), which matches option B.

Use the Given Row Transformation to Change the Matrix as Indicated