# seeking matlab mathod for solving it

• July 21st 2009, 10:31 PM
kurapati
seeking matlab mathod for solving it
Hi all,

I am wondering to know whether or not the following system of equations can be solved by matlab? If yes, could you please tell me how?

$A_1 X_1 = B_1 Y ; \\\\\\\
A_2 X_2 = B_2 Y ;

$

The matrices $A_1, A_2,B_1, B_2$ are 4 by 4 matrices. while the matrices $X_1,X_2,Y$ (unknown variables) are 4 by 1

I forgot to add this before : "The matrices X_1 and X_2 are made up of four variables of which the last three are same. The first one is different. and it is having a relation . The first variable in X_1 is say 'x_0' then the first variable in X_2 is [2-'x_0']"
I think : First solve for Y(dont know how) in the first equation and put it in the second equation.

Please help me how to solve the problem using matrix technique in the matlab
• July 22nd 2009, 04:46 AM
BobP
These equations don't have a specific solution do they ?
What you have here are eight equations (when you equate components in the two matrix equations) in twelve unknowns, (the components of the unknowns $X1, X2, \mbox{ and } Y$ ).
It looks like you need another matrix equation or to be content with a solution containing four parameters.
• July 22nd 2009, 07:58 AM
CaptainBlack
Quote:

Originally Posted by kurapati
Hi all,

I am wondering to know whether or not the following system of equations can be solved by matlab? If yes, could you please tell me how?

$A_1 X_1 = B_1 Y ; \\\\\\\
A_2 X_2 = B_2 Y ;

$

The matrices $A_1, A_2,B_1, B_2$ are 4 by 4 matrices. while the matrices $X_1,X_2,Y$ (unknown variables) are 4 by 1

I forgot to add this before : "The matrices X_1 and X_2 are made up of four variables of which the last three are same. The first one is different. and it is having a relation . The first variable in X_1 is say 'x_0' then the first variable in X_2 is [2-'x_0']"
I think : First solve for Y(dont know how) in the first equation and put it in the second equation.

Please help me how to solve the problem using matrix technique in the matlab

There is no unique solution (at least for non-singular $A_1$ and $B_2$) since if we choose any vector for $X_2$ we have:

$Y=B_2^{-1}A_2X_2$

and so:

$X_1=A_1^{-1}B_1B_2^{-1}A_2X_2$

CB
• July 22nd 2009, 09:46 PM
kurapati
Thanks for the replies.