MATLAB: Problem finding 2 unknown matrices in 2 equations

equationsmatricesmatrixsolveunknown

Hello,

I have 2 equations containing 2 unknown matrices of size nxn that I need to find. The equations looks like this.

I+R=E*T
B1-B1*R=E*B2*T

Where I is the Identity matrix og size nxn, and B1, B2 and E are known matrices of size nxn.

It seems like the built in solve functions doesnt work with matrices, and I cant seem to figure out how to solve it. Can anyone help with this?

Edit: I forgot to mention that the matrices B1 and B2 are diagonal matrices.

– Nicolai Hagelund

If you multiply the first equation by B1 and add the equations, you will eliminate R

 2*B1=(B1*E+E*B2)*T

You can then just solve for T linear algebraically (backslash) and then use equation (1) to obtain R.

You are almost there. What is the problem? Just use:

K=[a1 b1 c1;  
a1 b1 c2; 
a1 b2 c1; 
a1 b2 c2;  
a2 b1 c1; 
a2 b1 c2;
a2 b2 c1; 
a2 b2 c2 ]

Is this what you are looking for?

Have a look at the equations. If you rewrite them you will get:

Bw1 = ( b1 + b2 ) * 2*cos(2*w1) + b3 == 0;
Bw2 = ( b1 + b2 ) * 2*cos(2*w2) + b3 == 1;
Bw3 = ( b1 + b2 ) * 2*cos(2*w3) + b3 == 0;

That will explicitly show you that you can only solve for b3 and the sum of b2 and b1.

HTH