Question

Let $A=\left[a_{ij}\right]$ is a $3\times 3$ lower triangular matrix, then which of the following statement(s) is(are) correct

• A. maximum number of non-zero elements in $A$ are $7.$
• B. maximum number of distinct elements in $A$ are $7.$
• C. maximum number of non-zero elements in $A$ are $6.$
• D. maximum number of distinct elements in $A$ are $6.$

Answer 1

Answer: (B), (C)

maximum number of non-zero elements in $A$ are $6.$

Given : $A=\left[a_{ij}\right]$ is a $3\times 3$ lower triangular matrix.
We know, maximum number of non-zero elements lower/upper triangular matrix $=\frac{n^2+n}{2}=6$
and maximum number of distinct elements in lower/upper triangular matrix $=\frac{n^2+n}{2}+1=7.$