Chapter 3.1, Problem 40EQ

In each of the following, find the $6\times 6\text{ matrix }A=\left[a_{ij}\right]$ that satisfies the given condition:

$\begin{array}{l}\text{ (a) }{a}_{ij}=\{\begin{array}{cc}i+j& \text{ if }i\le j\\ 0& \text{ if }i>j\end{array}\text{ (b) }{a}_{ij}=\{\begin{array}{ll}1\hfill & \text{ if }|i-j|\le 1\hfill \\ 0\hfill & \text{ if }|i-j|>1\hfill \end{array}\hfill \\ \text{ (c) }{a}_{ij}=\{\begin{array}{ll}1\hfill & \text{ if }6\le i+j\le 8\hfill \\ 0\hfill & \text{ otherwise }\hfill \end{array}\hfill \end{array}$