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I have this series of operations. How can I obtain the matrix?

$$ K := E_{12}(27) \cdot E_{13}(2) \cdot E_{15}(7) \cdot E_{23}(23) \cdot E_{45}(3) \cdot E_{41}(12) \cdot E_{52}(2). $$

I tried to multiply from right to left (starting with the matrix I listed below). But I don't obtain the matrix I need.

I want to check with you if this is right:

$$ E_{52}(2)=\left[ \begin{array}{ c c } 1&0&0&0&0 \\ 0&1&0&0&0 \\ 0&0&1&0&0 \\ 0&0&0&1&0\\ 0&2&0&0&1 \end{array} \right] $$

Am I right?

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1 Answer 1

up vote 1 down vote accepted

I presume that your $E$'s are elementary matrices. So, $E_{52}(2)$ is as you have (put "2" in the $(5,2)$ position of the identity matrix $I$).

But this is just a guess... You should refer to your text/notes for the definition of the $E$'s.

Note that if the $E$'s are as described above, then multiplication of $A$ by one of these on the left (i.e., $EA$) corresponds to a row operation on $A$ (the same row operation needed to obtain $E$ from $I$).

Using this, you can compute $K$ in a manner less prone to arithmetic errors.

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Yes, E's are elementary matrices. I don't have an A. I have only these ones. So I should start with the $E_{52}(2)$ right? Instead of A –  Andrew Nov 29 '11 at 9:27
1  
Yes. Then multiply on the left by $E_{41}(12)$. So just take $E_{52}(2)$ and add 12 times row 1 to row 4. –  David Mitra Nov 29 '11 at 9:30

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