Question

Applying the following transformations will result in on the matrix in order on the matrix in order $\left[\begin{array}{ccc}1& 5& 2\\ 3& 1& 4\\ 2& 2& 3\end{array}\right]$

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Given matrix, $\left[\begin{array}{ccc}1& 5& 2\\ 3& 1& 4\\ 2& 2& 3\end{array}\right]$

$R_2\to R_2-R_3\to$ $\left[\begin{array}{ccc}1& 5& 2\\ 3-2& 1-2& 4-3\\ 2& 2& 3\end{array}\right]$

$\to$ $\left[\begin{array}{ccc}1& 5& 2\\ 1& -1& 1\\ 2& 2& 3\end{array}\right]$

$R_1\to R_1-R_2\to$ $\left[\begin{array}{ccc}1-1& 5+1& 2-1\\ 1& -1& 1\\ 2& 2& 3\end{array}\right]$

$\to$ $\left[\begin{array}{ccc}0& 6& 1\\ 1& -1& 1\\ 2& 2& 3\end{array}\right]$

$R_3-\to R_3-2R_2\to$ $\left[\begin{array}{ccc}0& 6& 1\\ 1& -1& 1\\ 0& -4& 1\end{array}\right]$