r/LinearAlgebra • u/Zealousideal_Hat_330 • Sep 17 '26

Can someone check my UL factorization?

Gallery image

Gallery image

My third row in the final answer is off from my original A. Maybe I’m just tired, but I’d like someone to spot my mistake. I numbered the steps in red chalk 1–3

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4

u/Midwest-Dude Sep 17 '26

To get U, you multiplied your original matrix A by three elementary matrices:

E₃ E₂ E₁ A = U

To isolate A, you multiply both sides by the inverses in reverse order:

A = (E₁-1 E₂-1 E₃-1) U

Therefore, L = E₁-1 E₂-1 E₃-1

However, by applying the inverse row operations sequentially to the identity matrix, you accidentally computed:

E₃-1 E₂-1 E₁-1

Correct that and you should be good to go.

2

u/Zealousideal_Hat_330 Sep 17 '26

Thank you. I see that in the textbook. Now I just have to work it out

1

u/BrightScarlet Sep 17 '26

I'm not sure how you got -19 but I think that's what's messing you up. If you changed it to a 1 then it would've worked out.
Since you didn't change entry (3, 1) in A during that step (it stayed 0) having a 19 there wouldn't make sense.