I am new to Mathematica and I try to apply the solution given to this [problem](https://math.stackexchange.com/questions/3328911/compute-the-inverse-of-a-matrix-with-partially-known-values).
So I have:

$$A = \begin{pmatrix}50 & 3 & 10 & 2\\\ 3 & 60 & 7 & 1\\\ 10 & 7 & 55 & 4\\\ 2 & 1 & 4 & 45 \end{pmatrix}$$

$$B = \begin{pmatrix}b\_{11} & b\_{12} & b\_{13} & 0\\\ b\_{12} & b\_{22} & 0 & 0\\\ b\_{13} & 0 & b\_{33} & b\_{34}\\\ 0 & 0 & b\_{34} & b\_{44} \end{pmatrix}$$

The idea is to invert $B$, and then solve the equations element-wise between the elements of $A$ and the elements of $B^{-1}$.
The invert of $B$ is:
[![B inverted](https://i.stack.imgur.com/7MWDj.png)](https://i.stack.imgur.com/7MWDj.png)

Code:

```
A = {{50, 3, 10, 2}, {3, 60, 7, 1}, {10, 7, 55, 4}, {2, 1, 4, 45}}
B = {{b11, b12, b13, 0}, {b12, b22, 0, 0}, {b13, 0, b33, b34}, {0, 0, 
      b34, b44}}
B2 = Inverse[B]

```

Now, I would like to solve the equations $B2\_{i, j} = A\_{i, j}$ to figure out the 7 parameters: $b\_{11}, b\_{12}, b\_{13}, b\_{22}, b\_{33}, b\_{34}, b\_{44}$. In other words, I want to get $B^{-1}\_{i, j}=A\_{i, j}$ if $B\_{ij} \neq 0$.

How can I solve this system of equations with Mathematica?

Bonus: Knowing that the actualy matrix have a shape of 16 per 16, and that there are 64 parameters $b\_{i, j}$, is this problem solvable with Mathematica or should I try something else?

Thanks for the help :)