how to find a matrix between linear equations

[Nir86]

hello,
I have four linear equations:
1. X_low = c1*X_up+d1
2. X_low = c2*Y_up+d2
3. Y_low = c3*X_up+d3
4. Y_low = c4*Y_up+d4

i know that [X_low ; Y_low] = A*[X_up ; Y_up] + B
how do I find matrix A and B?
thanks,

 

[Deleted member 4993]

hello,
I have four linear equations:
1. X_low = c1*X_up+d1
2. X_low = c2*Y_up+d2
3. Y_low = c3*X_up+d3
4. Y_low = c4*Y_up+d4

i know that [X_low ; Y_low] = A*[X_up ; Y_up] + B
how do I find matrix A and B?
thanks,

What is the difference between in X_low in (1) and X_low in (2)

Similarly:

What is the difference between in Y_low in (3) and Y_low in (4)

 

[Nir86]

What is the difference between in X_low in (1) and X_low in (2)

Similarly:

What is the difference between in Y_low in (3) and Y_low in (4)

it's the same value. but in the first equation there is a relationship between X_low and X_up and in the second equation there is a relationship between X_low and Y_up. i want to find a matrix that will describe the relationship between [X_up, Y_up] and [X_low, Y_low]

 

[blamocur]

You have 10 variables (4 x's and y's, 4 elements of A and 2 elements of B) and 6 equations (The matrix equation yields to linear equations). I do not think this system can have a unique solution.

 

[Dr.Peterson]

hello,
I have four linear equations:
1. X_low = c1*X_up+d1
2. X_low = c2*Y_up+d2
3. Y_low = c3*X_up+d3
4. Y_low = c4*Y_up+d4

i know that [X_low ; Y_low] = A*[X_up ; Y_up] + B
how do I find matrix A and B?
thanks,

The way I see this, the matrices A and B, between them, have 6 constants to be determined; you have four equations from which to find them, which I presume are to be identities, rather than to hold only for certain values of the X's and Y's.

But even more important, if you expand the matrix equation, you will get four equations which will contain only two distinct constant terms (the elements of B), so there will not always be a solution at all.

Where does this problem come from?