Question

please help!
Given the following matrix A, find an invertible matrix U so that A is equal to UR, when R is the reduced row-echelon form of A:

- i got the rref A but I cant multiply this with the A to get U. - please look at comment for matrix A

Answer 1

\[\left[\begin{matrix}2 & 2 & -6 & -12 \\ 1 & 4 & -6& -3 \\ -1 & 2 & 1 & 12\end{matrix}\right]\]

Answer 2

nice name. I can help you.

Answer 3

Wonderful! please do! I shall give you my rref A

Answer 4

I dont want the rref. You have to ref in a special way.

Answer 5

\[\left[\begin{matrix}1 & 0 & 0 & -1 \\ 0 & 1 & 0 & 4\\ 0 & 0 & 1 &0 \end{matrix}\right]\]

Answer 6

really? How so? you mean the augmented way with I?

Answer 7

no i'm going to show you and then explain. Im just going to write it on paper.

Answer 8

alright, Thanks!

Answer 9

I am sendin you a picture now but I didnt read the question carefully so there is more work to be done but I think its a start

Answer 10

hmmm interesting! totally different answer than mine for sure. But I do have to ask how did you get a 3x3 matrix from a 4x3

Answer 11

its a trick called LU factorization which I thought you were doing. Maybe you are but the question is a bit different from what ive seen before. Anyhow when you multiply a 3x3 by a 3x4 you still get a 3x4 matrix so its ok. if you look how i reduced it you see that I write the highest row first plus the lower rows and how much i have to multiply them by to get a zero in the front. once i get those reducations down I have an upper triangular matrix. now i need a lower triangular matrix so this trick i figured out is to first draw in the 0's and 1's down the diagonal and then take the coefficiants if front of the row operations and flip the sign and put it in the matrix it works every time.

Answer 12

interesting. thats very interesting.. so the method as you just said is how you would get the 3x3 matrix?

Answer 13

yes thats how i did it. When i was reading that chapter I remember that I couln't understand why it worked so i gave up trying to understand it and just used the method from the book and then i saw that this pattern came up so I've been showing that to other people and its good so far as long as you dont make a mistake.

Answer 14

thats right. yeah, I have never seen this method before, but it makes a lot of sense. So just to clarify, I got U as a 3 x 4 matrix. Is that correct?

Answer 15

ah, nvm. hah i misread it

Answer 16

Thanks a lot by the way

Answer 17

no problem. Don't you still need a rref matrix though or nah?

Answer 18

nah, it is alright. Thanks a lot

Answer 19

No problem. Now you got me wanting to figure it out anyway lol

Answer 20

hahah go ahead. thanks alot though. I apperciate it very much