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Q.
In a upper triangular matrix $n \times n$, minimum number of zeros is
Matrices
Solution:
As we know, a square matrix $A =\left[a_{i j}\right]$ is called an upper triangular matrix if $a_{i j}=0$ for all $i>j$
Such as, $A=\begin{bmatrix}1&2&3&4\\ 0&5&1&3\\ 0&0&2&9\\ 0&0&0&5\end{bmatrix}_{4 \times 4}$
Number of zeros $=\frac{4(4-1)}{2}=6=\frac{n(n-1)}{2}$.