Really simple matrix reduction

[NeonVomitt]

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

 

[rock.freak667]

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

 

[John Creighto]

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.

(A_1 A_2 A_3 A_4)^{-1}

gives what when the brackets are removed.

 

[NeonVomitt]

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)?