Linear Algebra - Elimination Matrix when Permutation Needed

[YoshiMoshi]

Homework Statement

I feel like I should know the answer to this, so I believe this to be an easy question. Say have matrix A, and I store the elimination matrices E_1,1 E_2,1 etc. and somewhere in the elimination process I have to use a permutation matrix to swap rows. My question is when I find the the final elimination matrix in which I multiply together all elimination matrices I used to get down to reduce row echelon form, do I also multiply by the permutation matrix?

Example:
I have [A] and than I multiply by E_1,1.
Then I multiply by E_2,1
Then I multiply by P_4,3 and am now in reduce row ecehlon form
when I go to find E is it
E = P_4,3 * E_2,1 * E_1,1
or is it just
E = E_2,1 * E_1,1

Thanks for any help.

Homework Equations

The Attempt at a Solution

 

[Ray Vickson]

Homework Statement

I feel like I should know the answer to this, so I believe this to be an easy question. Say have matrix A, and I store the elimination matrices E_1,1 E_2,1 etc. and somewhere in the elimination process I have to use a permutation matrix to swap rows. My question is when I find the the final elimination matrix in which I multiply together all elimination matrices I used to get down to reduce row echelon form, do I also multiply by the permutation matrix?

Example:
I have [A] and than I multiply by E_1,1.
Then I multiply by E_2,1
Then I multiply by P_4,3 and am now in reduce row ecehlon form
when I go to find E is it
E = P_4,3 * E_2,1 * E_1,1
or is it just
E = E_2,1 * E_1,1

Thanks for any help.

Homework Equations

The Attempt at a Solution

Since you needed to multiply by $P_{43}$ to get the final echelon form, the correct $E$ is the first one you wrote. Try it and see for yourself in an example.

 

[YoshiMoshi]

That's what my gut was telling me. Thanks for your help.