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# Advanced Math/Elementary matrices, column operations

Question
Consider the matrix

A = [[a, b, c],[d, e, f],[g, h, i]]

For each of the following elementary matrices E,

E_1= [[1, 0, 3],[0, 0, 1],[0, 1, 0]]

E_2= [[1, 0, 0],[0, 6, 0],[0, 0, 1]]

E_3 =[[1, 0, 0],[0, 0, 1],[0, 1, 0]]

-Compute AE.

-Multiplying by E on the right applies a "column operation" to A. Describe the column operation associated to E.

Hi, I am confused by the second part of the question. I have gotten the first parts, the one involving AE but I am confused about what to do for the second part.

For AE_1 :
[a,c,3a+b]
[d,f,3d+e]
[g,i,3g+h]

For AE_2 :
[a,6b,c]
[d,6e,f]
[g,6h,i]

For AE_3 :
[a,c,b]
[d,f,e]
[g,i,h]

For the second part of the question. I was thinking of lets say doing, usinf the example of A and E_3:
E_3A which would give:
[a,b,c]
[g,h,i]
[d,e,f]
and then i would say that the column opeation is that the 2nd and 3rd rows are interchanged.
I am really confused by this part, I do not know if this is correct. Any help would be greatly appreciated.

For your example of AE_3, it looks like this multiplication results in the 2nd and 3rd columns of A being interchanged. Since E_3 multiplies A on the right, this may be all the question is asking. Multiplying AE_3 again on the right to get your last result seems unnecessary, although it might be interesting in its own right when it comes to interpreting the operations of elementary matrices. Does this help?

Randy
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#### randy patton

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