Question

In a compact single dimensional array representation for lower triangular matrices (i.e. all the elements above the diagonal are zero) of size n $\times$ n, non-zero elements (i.e. elements of the lower triangle) of each row are stored one after another, starting from the first row, the index of the $(i,j{)}^{th}$ element of the lower triangular matrix in this new representation is

• A. $i+\frac{j(j-1)}{2}$
• B. $(j-1)+\frac{i(i-1)}{2}$
• C. $i+j-1$
• D. $i+j$

Answer 1

The correct option is B $(j-1)+\frac{i(i-1)}{2}$

LOC (i, j) formula of lower triangular matrix used
$=(j-1)+\frac{i(i-1)}{2}$