Finding Matrices E & F: A Matrix Challenge

[teme92]

Homework Statement

Find two matrices E and F such that:

EA=
\begin{bmatrix}
2 & 1 & 2\\
0 & 2 & 1\\
0 & 3 & 0\\
\end{bmatrix}

FA=
\begin{bmatrix}
0 & 2 & 1\\
0 & 3 & 0\\
2 & 7 & 2\\
\end{bmatrix}

Homework Equations

The Attempt at a Solution

So I know how to get the inverse of a 3x3 matrix and AxA^-1=I the identity matrix but I'm not sure how I approach this as I don't know what A is. Can anyone point me in the right direction here? Any help is much appreciated.

 

[verty]

Is there more to this problem? I think there is not enough information, A could be the identity matrix in which case it is trivial. A must be given for this to make any sense.

 

[teme92]

Ok I thought something was wrong with it alright. But to get E normally I'd just say:

EAA^-1=XA^-1

where X is the matrix giving. Is this correct?

 

[CAF123]

Ok I thought something was wrong with it alright. But to get E normally I'd just say:

EAA^-1=XA^-1

where X is the matrix giving. Is this correct?

Yes, provided A is in fact invertible.

 

[SammyS]

Homework Statement

Find two matrices E and F such that:

EA=
\begin{bmatrix}
2 & 1 & 2\\
0 & 2 & 1\\
0 & 3 & 0\\
\end{bmatrix}

FA=
\begin{bmatrix}
0 & 2 & 1\\
0 & 3 & 0\\
2 & 7 & 2\\
\end{bmatrix}

Homework Equations

The Attempt at a Solution

So I know how to get the inverse of a 3x3 matrix and AxA^-1=I the identity matrix but I'm not sure how I approach this as I don't know what A is. Can anyone point me in the right direction here? Any help is much appreciated.

Can you see any set of row operations which will transform matrix EA into matrix FA ?

 

[SammyS]

You may want to look at the determinant of EA and FA .