Row Echelon Form Homework - Finding Mistake

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Homework Help Overview

The discussion revolves around the process of converting a 3x3 matrix into row echelon form. The original poster is attempting to identify errors in their row operations while working with the matrix: [4 2 6], [2 8 2], [-1 3 1].

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster outlines their attempts at row operations but expresses confusion about where they went wrong. Some participants suggest specific row operations to simplify the matrix further. Others question the validity of the original poster's reasoning regarding the determinant and its implications for the LU decomposition.

Discussion Status

The discussion is ongoing, with participants providing guidance on potential next steps for the row operations. There is a divergence in focus, with some exploring the row echelon form while others delve into the implications for LU decomposition and determinants. No consensus has been reached regarding the original poster's errors.

Contextual Notes

The original poster mentions the goal of finding the LU decomposition, which introduces additional constraints related to the determinants of the matrices involved. There is also a reference to specific numerical values that may influence the discussion.

Chadlee88
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Homework Statement


i'm trying to put the 3x3 matrix: [4 2 6]
[ 2 8 2]
[-1 3 1]
into row echelow from.
but i don't know where I'm goin wrong in my row operations. could some1 please tell me where i have made the mistake.





Homework Equations





The Attempt at a Solution



[4 2 6] [4 2 6 ] [4 2 6]
[2 8 2] r2->r2+2r3 [0 14 4] r3-> 4r3 [0 14 4]
[-1 3 1] [-1 3 1] [-4 12 4]


r3->r3+r1 [4 2 6 ] r3->r3-r2 [4 2 6]
[0 14 4] [0 14 4] :confused:
[0 14 10 [0 0 6]
 
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Divide the second row by 14, then subtract twice the second row from the first row. Figure out the rest from there
 
What makes you think that that's wrong? With a few more operations you can get to I (the identity matrix) if that's what you need.
 
? I'm trying to find the LU decomposition so U is jst an upper triangular matrix and that's what my answer above is. and from the fact that
det(A) = det(LU) = det(L)det(U) = det(U) as det(L) = 1 the determinant of A has to be equal to the determinant of U. i worked out the determinant of A to be 84 but the determinant of U = 4((14x6)-(4x0))-2((0x6)-(4x0))+6((0x0)-(14x0)) = 4x14x6 = 336 which does not equal 84! i still dont' get what I've done wrong :(
 

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