Inverse of Matrix Sum Formula: Solving for Upper Triangular Matrices

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Physics_wiz
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Does anyone know a formula for the inverse of a sum of two upper triangular matrices?
 
What makes you think there is such a formula?

Have you looked at the inverse of
[tex]\left(\begin{array}{cc}a & b \\ 0 & c\end{array}\right)+ \left(\begin{array}{cc}x & y \\ 0 & z\end{array}\right)[/tex]?