Question

If $A$ is a $3^{rd}$ order square matrix whose general element $a_{ij} = \frac{2i-j}{2}$ and $A = L + D + U$ where $L, D \& U$ are Lower triangular, diagonal and upper triangular matrices. Then the sum of non-diagonal elements of the matrix $L$ is _______

Answer 1

6

Answer 2

The matrix $A$ is constructed using the given formula $a_{ij} = \frac{2i-j}{2}$. In the decomposition $A=L+D+U$, $L$ contains the elements of $A$ below the main diagonal. The non-diagonal elements of $L$ are precisely these elements: $l_{21}, l_{31}, l_{32}$. Their sum is calculated directly.