Given the matrix R $$\mathbf { R } = \left[ \begin{array} { c c c | c }
1 & - 3 & 0 & - 5 \
- 2 & 1 & 5 & 1 \
5 & 0 & 1 & - 4
\end{array} \right]$$ write the matrix obtained after executing the following elementary row operations: i). First, multiply the first row by 2 and add the result to the second row.
Ii)) Then, multiply the first row by -5 and add the result to the third row.
A)
$\left[ \begin{array} { l l l | l } 1 & - 3 & 0 & - 5 \ 0 & - 5 & 5 & - 9 \ 0 & 15 & 1 & 21 \end{array} \right]$
B)
$\left[ \begin{array} { c c c | c }
1 & - 3 & 0 & - 5 \
0 & 7 & 5 & 11 \
0 & - 15 & 1 & - 29
\end{array} \right]$
C)
$\left[ \begin{array} { c c c | c } 1 & - 3 & 0 & - 5 \ 0 & - 5 & 5 & - 9 \ 0 & 0 & 1 & 21 \end{array} \right]$

D)
$\left[ \begin{array} { c c c | c } 1 & - 3 & 0 & - 5 \ 0 & - 5 & 5 & - 9 \ 0 & 0 & 1 & - 29 \end{array} \right]$

Question

Given the matrix R $$\mathbf { R } = \left[ \begin{array} { c c c | c } 
1 & - 3 & 0 & - 5 \
- 2 & 1 & 5 & 1 \
5 & 0 & 1 & - 4
\end{array} \right]$$ write the matrix obtained after executing the following elementary row operations: i). First, multiply the first row by 2 and add the result to the second row.
Ii)) Then, multiply the first row by -5 and add the result to the third row. 
A)
$\left[ \begin{array} { l l l | l } 1 & - 3 & 0 & - 5 \ 0 & - 5 & 5 & - 9 \ 0 & 15 & 1 & 21 \end{array} \right]$
B)
$\left[ \begin{array} { c c c | c } 
1 & - 3 & 0 & - 5 \
0 & 7 & 5 & 11 \
0 & - 15 & 1 & - 29
\end{array} \right]$
C)
$\left[ \begin{array} { c c c | c } 1 & - 3 & 0 & - 5 \ 0 & - 5 & 5 & - 9 \ 0 & 0 & 1 & 21 \end{array} \right]$

D)
$\left[ \begin{array} { c c c | c } 1 & - 3 & 0 & - 5 \ 0 & - 5 & 5 & - 9 \ 0 & 0 & 1 & - 29 \end{array} \right]$

Quizplus · Accepted Answer

The correct operations are applied as follows: i) Multiplying the first row by 2 gives [2, -6, 0, -10]. Adding this to the second row results in [0, -5, 5, -9]. ii) Multiplying the first row by -5 gives [-5, 15, 0, 25]. Adding this to the third row results in [0, 15, 1, 21].

Given the Matrix R R=[1−30−5−2151501−4]\mathbf { R } = \left[ \begin{array} { c c c | c } 1 & - 3 & 0 & - 5 \\- 2 & 1 & 5 & 1 \\5 & 0 & 1 & - 4\end{array} \right]R=​1−25​−310​051​−51−4​​

Given the Matrix R $\mathbf { R } = \left[ \begin{array} { c c c | c } 1 & - 3 & 0 & - 5 \\- 2 & 1 & 5 & 1 \\5 & 0 & 1 & - 4\end{array} \right]$