
1.4.1 Matrix transformations
Problem:
Find inverse matrix to matrix \( A \) of size \( \times n \)
\[
\left(\begin{array}{cccccc}
n & n-1 & n-2 & \ldots & 2 & 1 \\
1 & n-1 & n-2 & \ldots & 2 & 1 \\
1 & 1 & n-2 & \ldots & 2 & 1 \\
\ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\
1 & 1 & 1 & \ldots & 2 & 1 \\
1 & 1 & 1 & \ldots & 1 & 1
\end{array}\right) .
\]