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Really simple matrix reduction

  • Thread starter NeonVomitt
  • Start date
1. 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!


2. Homework Equations


THANKS
3. The Attempt at a Solution
 

rock.freak667

Homework Helper
6,230
31
the product of the matrices at the end of each step should give back the original matrix.
 
1. 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.
 
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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