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

Multiple Choice

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