Question

Construct a $3\times 3$ matrix whose elements $a_{ij}$ are given by $a_{ij}=0$ if $i\ne j$ and $a_{ij}=-8$ if $i=j$.

Answer 1

The elements of a $3\times 3$ matrix are: $A=\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right]$

Applying the given rule: $a_{ij}=0$ if $i\ne j$ and $a_{ij}=-8$ if $i=j$.
$a_{11}=-8,a_{12}=0,a_{13}=0a_{21}=0,a_{22}=-8,a_{23}=0a_{31}=0,a_{32}=0,a_{33}=-8$

$A=\left(\begin{array}{ccc}-8& 0& 0\\ 0& -8& 0\\ 0& 0& -8\end{array}\right)$ is the required matrix