Answer it by using Python.

$10\mathrm{.}17$ Patients and symptoms. Each of a set of $N$ patients can exhibit any number of a set of $n$

symptoms. We express this as an $Nn$ matrix $S,$ with

$S_{ij}=\{\begin{array}{ccc}1& \text{p}\text{a}\text{t}\text{i}\text{e}\text{n}\text{t}\text{i}\text{e}\text{x}\text{h}\text{i}\text{b}\text{i}\text{t}\text{s}\text{s}\text{y}\text{m}\text{p}\text{t}\text{o}\text{m}& j\\ 0& \text{p}\text{a}\text{t}\text{i}\text{e}\text{n}\text{t}\text{i}\text{d}\text{o}\text{e}\text{s}\text{n}\text{o}\text{t}\text{e}\text{x}\text{h}\text{i}\text{b}\text{i}\text{t}\text{s}\text{y}\text{m}\text{p}\text{t}\text{o}\text{m}& j.\end{array}$

Give simple English descriptions of the following expressions. Include the dimensions,

and describe the entries.

$($a$)S1.$

$($b$)S^{T}1.$

$($c$)S^{T}S.$

$($d$)S{S}^T.$