Really simple matrix reduction

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    Matrix Reduction
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Homework Help Overview

The discussion revolves around matrix reduction, specifically focusing on expressing a given matrix A as a product of elementary matrices. The original poster seeks assistance with two tasks: writing A as a product of four elementary matrices and finding the inverse of A expressed similarly.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the concept of elementary matrices and their relation to row operations on the identity matrix. There is a focus on the need to express row operations as matrices rather than just performing them. Questions arise about the correctness of the steps taken and the interpretation of the tasks.

Discussion Status

Participants are actively exploring the steps involved in expressing the matrix A and its inverse as products of elementary matrices. Some guidance has been offered regarding the need to represent row operations as matrices, and there is an ongoing examination of the steps provided by participants.

Contextual Notes

There is a mention of potential confusion regarding the requirements of the tasks, particularly in how to express the row operations and the resulting matrices. Participants are questioning their understanding of the definitions and processes involved in matrix reduction and inversion.

NeonVomitt
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Homework Statement



I don't know why I keep getting this wrong...some help would be greatly appreciated.

A =

[ 0 -6 ]
[-2 -3 ]

(1) Write A as a product of 4 elementary matrices:

Wouldn't that just mean to Reduce Row echelon it, and show it in 4 steps?

(2) Write A^-1 as a product of 4 elementary matrices

Wouldn't I just find the inverse of A, and write down the steps?

I did all that and I got it wrong...so maybe if someone could show me, it would really help me out!


Homework Equations




THANKS

The Attempt at a Solution

 
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the product of the matrices at the end of each step should give back the original matrix.
 
NeonVomitt said:

Homework Statement



I don't know why I keep getting this wrong...some help would be greatly appreciated.

A =

[ 0 -6 ]
[-2 -3 ]

(1) Write A as a product of 4 elementary matrices:

In this case an elementary matrix means a matrix which you obtain by preforming a single row operation on the identity matrix.

Wouldn't that just mean to Reduce Row echelon it, and show it in 4 steps?
Yes but you have to express the row operations as a matrix.

(2) Write A^-1 as a product of 4 elementary matrices

Wouldn't I just find the inverse of A, and write down the steps?
Remember A is expressed as the product of four elementary matrices.

[tex](A_1 A_2 A_3 A_4)^{-1}[/tex]

gives what when the brackets are removed.
 
rock.freak667 said:
the product of the matrices at the end of each step should give back the original matrix.

that is what RREF does anyways.

So if,

[ -2 -3 ]
[ 0 -6]

[1 3/2 ]
[0 -6 ]

[ 1 3/2 ]
[ 0 1 ]

[1 0 ]
[0 1 ]

Is that not the answer in four elementary matrix steps for the first question?

And for the second question it is the same, but steps on the other side (inverse matrix)?
 

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