[Matrix Manipulation] Help plz!

[Adun]

Assuming
\[P=\left[\begin{array}{cc}A & B \\C & D\end{array}\right]\]
and
\[Q=\left[\begin{array}{cc}D & B \\C & A\end{array}\right]\]
where A, B, C, D are unknown.

It's also known that
\[P\times M\times Q=T1\]
\[P\times X\times Q=T2\]
where X is unknown
M, T1 and T2 are known.

All the matrices are 2-by-2 matrix

So is there a way to find out X?

I tried to solve A,B,C,D first by 2nd order equations. But it is too complex even for Maple.

So I am wondering if there is a way to find out X by matrix manipulation?

Thank you very much!

 

[LouisSheffield]

I don't see "X" appearing in your equations - please revise them!

 

[Adun]

I don't see "X" appearing in your equations - please revise them!

Hi Louis the 'X' is in the equation \[P\times X\times Q=T2\]

 

[mayyan]

PXQ = T2

If P,Q,T2 are known we can get 4 equations with 4 parameters so you should be able to solve it.

 

[mkhan]

Hi,

with A,B,C,D and X unknown , u get 8 unknown variables, and u get four equations (isnt it?). can we solve it? I dont think so.

Arif

 

[mayyan]

Hi,

with A,B,C,D and X unknown , u get 8 unknown variables, and u get four equations (isnt it?). can we solve it? I dont think so.

Arif

as far as i understand A,B,C,D are known parameters so there is no problem. if its not just use the first equation so you will have 8 equation with 8 unknown.

 

[mkhan]

Hi,

******************************************************
Assuming

and

where A, B, C, D are unknown.

It's also known that


where X is unknown
M, T1 and T2 are known.
****************************************************

I think it is clear in message that A, B, C, D and X are "UNKNOWN". Isnt it?

Arif

 

[jody]

Hi , I think ask for this is ' X = T2 * inv(P*Q) '

 

[Adun]

A,B,C,D (hence P,Q) and X are all unknown...

 

[nandhika]

hi

i agree to jodi
first multiply P and Q the result is R suppose

then multiply T2 with inverse matrix of R.........

 

[mayyan]

Hi , I think ask for this is ' X = T2 * inv(P*Q) '

it isnt not posible to do that unless you prove an inverse P,Q exsist.

 

[prasanth]

i think it is not possible to find X...