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How can we solve this matricial system?
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The exercise:
Solve the system of matricial equations
$MAX+NY=M$
$NAX+PY=N$
I am trying to​ determine $X$ and $Y$, but I know I can't use something like $M^-1$ or $N^-1$ because I don't know if the matrices are invertible. I think I have to somehow isolate one variable in one equation and substitute it on the other, but I was not able to find any content explaining exercises like this one.
matrices
asked Jul 19 at 0:36
Alexandre Tourinho
1305
add a comment |Â
up vote
0
down vote
favorite
The exercise:
Solve the system of matricial equations
$MAX+NY=M$
$NAX+PY=N$
I am trying to​ determine $X$ and $Y$, but I know I can't use something like $M^-1$ or $N^-1$ because I don't know if the matrices are invertible. I think I have to somehow isolate one variable in one equation and substitute it on the other, but I was not able to find any content explaining exercises like this one.
matrices
asked Jul 19 at 0:36
Alexandre Tourinho
1305
Is there any relationship between $M$ and $A$?
– Eben Cowley
Jul 19 at 2:12
The exercise says nothing about a relation between $M$ and $A$. Where I found the question, the answear is illegible. Do you know what should I search to find any content about this exercise?
– Alexandre Tourinho
Jul 19 at 13:12
Honestly I've never seen a linear algebra exercise like this. It's really just a system of $2n^2$ ordinary real linear equations, but I don't see a quick way to solve it unless M and N are invertible. Perhaps thinking about the system as being of the form $TV=W$ where T is a $2n^2 times 2n^2$ matrix and the other two are vectors in $2n^2$ dimensions will be fruitful, although tedious.
– Eben Cowley
Jul 19 at 17:47
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
The exercise:
Solve the system of matricial equations
$MAX+NY=M$
$NAX+PY=N$
I am trying to​ determine $X$ and $Y$, but I know I can't use something like $M^-1$ or $N^-1$ because I don't know if the matrices are invertible. I think I have to somehow isolate one variable in one equation and substitute it on the other, but I was not able to find any content explaining exercises like this one.
matrices
asked Jul 19 at 0:36
Alexandre Tourinho
1305
The exercise:
Solve the system of matricial equations
$MAX+NY=M$
$NAX+PY=N$
I am trying to​ determine $X$ and $Y$, but I know I can't use something like $M^-1$ or $N^-1$ because I don't know if the matrices are invertible. I think I have to somehow isolate one variable in one equation and substitute it on the other, but I was not able to find any content explaining exercises like this one.
matrices
asked Jul 19 at 0:36
Alexandre Tourinho
1305
asked Jul 19 at 0:36
Alexandre Tourinho
1305
asked Jul 19 at 0:36
Alexandre Tourinho
1305
asked Jul 19 at 0:36
Alexandre Tourinho
1305
1305
Is there any relationship between $M$ and $A$?
– Eben Cowley
Jul 19 at 2:12
The exercise says nothing about a relation between $M$ and $A$. Where I found the question, the answear is illegible. Do you know what should I search to find any content about this exercise?
– Alexandre Tourinho
Jul 19 at 13:12
Honestly I've never seen a linear algebra exercise like this. It's really just a system of $2n^2$ ordinary real linear equations, but I don't see a quick way to solve it unless M and N are invertible. Perhaps thinking about the system as being of the form $TV=W$ where T is a $2n^2 times 2n^2$ matrix and the other two are vectors in $2n^2$ dimensions will be fruitful, although tedious.
– Eben Cowley
Jul 19 at 17:47
add a comment |Â
Is there any relationship between $M$ and $A$?
– Eben Cowley
Jul 19 at 2:12
The exercise says nothing about a relation between $M$ and $A$. Where I found the question, the answear is illegible. Do you know what should I search to find any content about this exercise?
– Alexandre Tourinho
Jul 19 at 13:12
Honestly I've never seen a linear algebra exercise like this. It's really just a system of $2n^2$ ordinary real linear equations, but I don't see a quick way to solve it unless M and N are invertible. Perhaps thinking about the system as being of the form $TV=W$ where T is a $2n^2 times 2n^2$ matrix and the other two are vectors in $2n^2$ dimensions will be fruitful, although tedious.
– Eben Cowley
Jul 19 at 17:47
Is there any relationship between $M$ and $A$?
– Eben Cowley
Jul 19 at 2:12
Is there any relationship between $M$ and $A$?
– Eben Cowley
Jul 19 at 2:12
The exercise says nothing about a relation between $M$ and $A$. Where I found the question, the answear is illegible. Do you know what should I search to find any content about this exercise?
– Alexandre Tourinho
Jul 19 at 13:12
The exercise says nothing about a relation between $M$ and $A$. Where I found the question, the answear is illegible. Do you know what should I search to find any content about this exercise?
– Alexandre Tourinho
Jul 19 at 13:12
Honestly I've never seen a linear algebra exercise like this. It's really just a system of $2n^2$ ordinary real linear equations, but I don't see a quick way to solve it unless M and N are invertible. Perhaps thinking about the system as being of the form $TV=W$ where T is a $2n^2 times 2n^2$ matrix and the other two are vectors in $2n^2$ dimensions will be fruitful, although tedious.
– Eben Cowley
Jul 19 at 17:47
Honestly I've never seen a linear algebra exercise like this. It's really just a system of $2n^2$ ordinary real linear equations, but I don't see a quick way to solve it unless M and N are invertible. Perhaps thinking about the system as being of the form $TV=W$ where T is a $2n^2 times 2n^2$ matrix and the other two are vectors in $2n^2$ dimensions will be fruitful, although tedious.
– Eben Cowley
Jul 19 at 17:47
add a comment |Â
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Is there any relationship between $M$ and $A$?
– Eben Cowley
Jul 19 at 2:12
The exercise says nothing about a relation between $M$ and $A$. Where I found the question, the answear is illegible. Do you know what should I search to find any content about this exercise?
– Alexandre Tourinho
Jul 19 at 13:12
Honestly I've never seen a linear algebra exercise like this. It's really just a system of $2n^2$ ordinary real linear equations, but I don't see a quick way to solve it unless M and N are invertible. Perhaps thinking about the system as being of the form $TV=W$ where T is a $2n^2 times 2n^2$ matrix and the other two are vectors in $2n^2$ dimensions will be fruitful, although tedious.
– Eben Cowley
Jul 19 at 17:47