I have a question, which I have changed slightly, but I do not understand 'the phrasing' of the question and the notation used:
$Q:$ Write explicitly the matrix $\mathbf{W} = [w_{ij}] $, where $ [w_{ij}] =i^2 +j$. ( $\mathbf{W} $ is a $3 \times 3 $ matrix).
I do not understand the phrase 'explicitly'. I think the question means repersent the matrix $\mathbf{W} $, using the definition, generally?
And i do not understand the notation '$\mathbf{W} = [w_{ij}] $'.
I thought the notation above meant the $i$-th row and the $j$-th column? Crucially, how are you meant to define a matrix, given $ [w_{ij}] =i^2 +j$?
It asks you to write out all elements of $$\left[\begin{array}{ccc}w_{11}&w_{12}&w_{13}\\w_{21}&w_{22}&w_{23}\\w_{31}&w_{32}&w_{33}\end{array}\right]$$ explicitly.
For example, $$w_{12}=1^2+2=3.$$