Are you trying to solve for a, b,c variables in terms of a numerical matrix T or the problem is to obtain T as the unknown?

Debopam Ghosh

The problem is to obtain T as the unknown. In this case, T is a 3*3 matrix with 9 variables.

Hi Liming Yuan,

Are you looking for the algorithm to compute the Matrix {T}?

If you have studied linear algebra previously, there are only 4 variables instead of 9 in the Matrix {T}

{T} = [p q 0; r s 0; 0 1 1]

Yew-Chung Chak

Yes, I'm looking for the algorithm that can derive the generalized expression of T, where a,b,c are arbitrary real numbers.

OK. I give you the algorithm. But you have to figure out the solution by yourself as part of your learning process.

p = a2 / (a + b)

q = r = a*b / (a + b)

s = b2 / (a + b)

provided that a + b ≠ 0, and c ≠ 0.

Yew-Chung Chak

Your solution doesn't seem correct. I find if p=r=a/(a+b), q=s=b/(a+b), then this equation holds. However, I do not think it's a general solution. For example, when T =[1 a/b 0;0 0 0;0 1 1], this equation still holds.

T= ( 1 0 0 ; 0 1 0 ; 0 1 1 ) regardless of a , b, c precise numerical values.

Hi Liming Yuan,

Typos in the previous equations. And Debopam Ghosh is correct.

p = a2 / (a2 + b2)

q = r = a*b / (a2 + b2)

s = b2 / (a2 + b2)

provided that a2 + b2 ≠ 0, and c ≠ 0.

By the way, do you really understand how the Matrix {T} works?

Yew-Chung Chak

If

p = a2 / (a2 + b2)

q = r = a*b / (a2 + b2)

s = b2 / (a2 + b2)

Then [a b 0;0 0 c]*T=[(a3+ab2)/(a+b) (a2b+b3)/(a+b);0 c c]. It's not right.

So I think p=r=a/(a+b), q=s=b/(a+b) .

Debopam Ghosh gives a specific answer.

My purpose is to find a algorithm to derive a general expression of such equations.

It's not difficult to solve it by hand through linear equations.

Hi Liming Yuan,

I've no idea how you obtained that. Perhaps there is a bug in the computation.

Thank you, Yew-Chung Chak .

I found my mistake.