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Math Help - Find elementary matrix E such that AB=EB

  1. #1
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    Find elementary matrix E such that AB=EB

    Any help is appreciated!
    Attached Thumbnails Attached Thumbnails Find elementary matrix E such that AB=EB-capture7.jpg  
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  2. #2
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    Try:
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  3. #3
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    <br /> <br />
im(B)=span(\begin{bmatrix}-1 \\1 \end{bmatrix})~,~<br />
AB-EB=0\rightarrow (A-E)B=0\rightarrow <br />
\begin{bmatrix}-1 \\1 \end{bmatrix} \in ker(A-E)<br /> <br />

    If suppose  A-E= \begin{bmatrix}1&1 \\1&1 \end{bmatrix}<br />
\rightarrow E=\begin{bmatrix}-1&0 \\-1&0 \end{bmatrix}<br /> <br />
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  4. #4
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    Quote Originally Posted by math2009 View Post
    <br /> <br />
im(B)=span(\begin{bmatrix}-1 \\1 \end{bmatrix})~,~<br />
AB-EB=0\rightarrow (A-E)B=0\rightarrow <br />
\begin{bmatrix}-1 \\1 \end{bmatrix} \in ker(A-E)<br /> <br />

    If suppose  A-E= \begin{bmatrix}1&1 \\1&1 \end{bmatrix}<br />
\rightarrow E=\begin{bmatrix}-1&0 \\-1&0 \end{bmatrix}<br /> <br />
    That is NOT an elementary matrix.
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