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Exercise 3.2.12

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If $B^{'}$ can be transformed into $D^{'}$ by an elementary row operation, we could write $D^{'} = E B^{'}$ by some elementary matrix $E$ . Let

E^{'} = (\begin{matrix} 1 & 0 & \dots & 0 \\ 0 \\ ⋮ & B^{'} \\ 0 \end{matrix})

be an larger matrix. Then we have $D = E^{'} B$ and hence $D$ can be obtained from $B$ by an elementary row operation. For the version of column, we have $D^{'} = B^{'} E$ . And then get the matrix $E^{'}$ by the same way. Finally we have $D = B E^{'}$ .

jephianlin

2011-06-27 00:00

Exercise 3.2.12

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