## 每週問題 April 28, 2014

Let

$\displaystyle A=\left[\!\!\begin{array}{rcr} 1&1&2\\ 1&2&1\\ -1&1&-1 \end{array}\!\!\right]\begin{bmatrix} 0&0&0\\ 0&3&0\\ 0&0&5 \end{bmatrix}\left[\!\!\begin{array}{rcr} 1&1&2\\ 1&2&1\\ -1&1&-1 \end{array}\!\!\right]^{-1}$.

Determine the reduced row echelon form of $A$.

$\displaystyle \left\{\left[\!\!\begin{array}{r} -1\\ 1\\ 0 \end{array}\!\!\right],\left[\!\!\begin{array}{c} 1\\ 0\\ 1 \end{array}\!\!\right]\right\}$

$\displaystyle B=\left[\!\!\begin{array}{rcc} -1&1&0\\ 1&0&1\\ 0&0&0 \end{array}\!\!\right]$

$\displaystyle \left[\!\!\begin{array}{ccc} 1&0&1\\ 0&1&1\\ 0&0&0 \end{array}\!\!\right]$

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