91影视

Interchanging the row $2$and $3$, we get:

$\left[\begin{array}{rrrr}1& -3& -2& 4\\ 2& 2& -1& -3\\ 4& -2& -3& -1\end{array}\right]\stackrel{R_2鈫�R_3}{鉄�}\left[\begin{array}{rrrr}1& -3& -2& 4\\ 4& -2& -3& -1\\ 2& 2& -1& -3\end{array}\right]$

Thus, the desired matrix isrole="math" localid="1644563132030" $\left[\begin{array}{rrrr}1& -3& -2& 4\\ 4& -2& -3& -1\\ 2& 2& -1& -3\end{array}\right]$

Multiplying the row $1$by$2$, we get:

role="math" localid="1644562042821" $$\begin{gathered} \left[\begin{array}{rrrr}1& -3& -2& 4\\ 2& 2& -1& -3\\ 4& -2& -3& -1\end{array}\right]\stackrel{2R_1}{鉄�}\left[\begin{array}{cccc}2路1& 2(-3)& 2(-2)& 2路4\\ 2& 2& -1& -3\\ 4& -2& -3& -1\end{array}\right] \\ =\left[\begin{array}{cccc}2& -6& -4& 8\\ 2& 2& -1& -3\\ 4& -2& -3& -1\end{array}\right] \end{gathered}$$

The resultant matrix is:

role="math" localid="1644563166851" $\left[\begin{array}{cccc}2& -6& -4& 8\\ 2& 2& -1& -3\\ 4& -2& -3& -1\end{array}\right]$

First, multiplying the row $3$by $2$, we get:

role="math" localid="1644562922802" $$\begin{gathered} \left[\begin{array}{rrrr}1& -3& -2& 4\\ 2& 2& -1& -3\\ 4& -2& -3& -1\end{array}\right]\stackrel{-2R_3}{鉄�}\left[\begin{array}{rrrr}1& -3& -2& 4\\ 2& 2& -1& -3\\ 4(-2)& -2(-2)& -3(-2)& -1(-2)\end{array}\right] \\ =\left[\begin{array}{llll}1& -3& -2& 4\\ 2& 2& 2& -10\\ -8& 4& 6& 2\end{array}\right] \end{gathered}$$

Now add the row $3$and $2$, we get:

$$\begin{gathered} \left[\begin{array}{llll}1& -3& -2& 4\\ 2& 2& 2& -10\\ -8& 4& 6& 2\end{array}\right]\stackrel{R_2鈫�R_2+R_3}{鈫�}\left[\begin{array}{llll}1& -3& -2& 4\\ 2+(-8)& 2+4& 2+6& -10+2\\ -8& 4& 6& 2\end{array}\right] \\ =\left[\begin{array}{llll}1& -3& -2& 4\\ -6& 6& 8& -8\\ -8& 4& 6& 2\end{array}\right] \end{gathered}$$

The resultant matrix is:

role="math" localid="1644563236470" $\left[\begin{array}{llll}1& -3& -2& 4\\ -6& 6& 8& -8\\ -8& 4& 6& 2\end{array}\right]$