Question

Let $A=\left[a_{ij}\right]$ is a $5\times 5$ upper triangular matrix, then which of the following statement(s) is(are) correct

• A. Minimum number of zeros in $A$ are $15.$
• B. Minimum number of zeros in $A$ are $10.$
• C. Maximum number of zeros in $A$ are $25.$
• D. Maximum number of zeros in $A$ are $24.$

Answer 1

Answer: (B), (D)

Maximum number of zeros in $A$ are $24.$

Given : $A=\left[a_{ij}\right]$ is a $5\times 5$ upper triangular matrix.
We know, minimum number of zeros in upper triangular matrix $=\frac{n^2-n}{2}=10$
and maximum number of zeros $=n^2-1=24$.