Finding Matrices E & F: A Matrix Challenge

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Homework Help Overview

The problem involves finding two matrices E and F such that their products with an unknown matrix A yield specified resultant matrices. The context is centered around matrix operations and properties, particularly involving matrix multiplication and potential inverses.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants express uncertainty about the lack of information regarding matrix A, questioning whether it could be the identity matrix. There are attempts to derive E and F using properties of matrix inverses and row operations, with some participants suggesting that additional information is necessary to proceed.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some have proposed potential methods for finding E and F, while others emphasize the need for clarity regarding matrix A. Suggestions for examining row operations and determinants have been made, indicating a productive exploration of the problem.

Contextual Notes

There is a noted lack of information about matrix A, which is critical for solving the problem. Participants are also considering the implications of A being invertible.

teme92
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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.
 
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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.
 
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?
 
teme92 said:
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.
 
teme92 said:

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

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