# The reduced row echelon form of the matrix A is begin{bmatrix}1 & 2&0 0 & 0&10&0&0 end{bmatrix} Find three different such matrices A. Explain how you determined your matrices.

The reduced row echelon form of the matrix A is
$\left[\begin{array}{ccc}1& 2& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right]$
Find three different such matrices A. Explain how you determined your matrices.
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pierretteA
Step 1
The given matrix is $\left[\begin{array}{ccc}1& 2& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right]$
Multiply the first row by 2 and obtain $\left[\begin{array}{ccc}2& 4& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right]$
Multiply the second row by 2 and obtain $\left[\begin{array}{ccc}1& 2& 0\\ 0& 0& 2\\ 0& 0& 0\end{array}\right]$
Step 2
Add first and second row of $\left[\begin{array}{ccc}1& 2& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right]$ and substitute the result into 3rd row.
That is, $\left[\begin{array}{ccc}1& 2& 0\\ 0& 0& 1\\ 1& 2& 1\end{array}\right]$
Thus, three different such matrices are
These matrices are obtained by performing some elementary row operations on $\left[\begin{array}{ccc}1& 2& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right]$
Jeffrey Jordon