Question $4.(0,1)$ Matrices

Read the material on $(0,1)$ Matrices in Section $2\mathrm{.}2,$ pp$.112-115$ in the text and work through Practice

Problem #$3$ on page $115.$ The following questions refer to Exercise #$26$ on page $121$ of the text. You should

work through parts $($a$)-($e$)$ of Exercise #$26$ on your own $($no writeup necessary$).$ Then use hand calculations

and Matlab to write up answers to the following questions.

Enter the $66$ matrix A given before part $($f$)$ into your MATLAB workspace $($be careful to copy A correctly$).$

$($i$)$ On a plain sheet of paper draw by hand six vertices labeled $1-6($one for each person$).$ Make this into

a directed graph by putting an arrow pointing from vertex $i$ to vertex $j$ for all ordered pairs $(i,j)$ for which

the entry $a_{ij}=1$ in $A.$

Either scan it or take a picture of your graph and submit it$.$ Make sure it is in $.$jpg$/.$jpeg or $.$pdf formats.

Give detailed solutions in your lab report for the following.

$($ii$)$ Answer part $($f$)$ of Exercise #$26.$ Obtain the answer in two ways: by the graph and by the matrix $A.$

Give details.

$($iii$)$ Answer part $($g$)$ of Exercise #$26.$ Use the matrices $A,A^2,A^3,$ and $A^4$ to obtain your answer and

consider the four cases $(1,2,3,4$ stages$)$ separately. Give details.

$($iv$)$ Answer part $($h$)$ of Exercise #$26.$ Use the matrix $B=A+A^2+A^3+A^4$ to obtain your answer. Give

details.

Final Editing of Lab Write$-$up: After you have worked through all the parts of the lab assignment,

you will need to edit your diary file. Remove all typing errors. Your write$-$up should only contain the

input commands that you typed and the output results generated by MATLAB, together with your answers

to the questions. In particular, remove from your diary file any of the results generated by the load,

save, clear, format, help commands that you used. Preview the document before printing and remove

unnecessary page breaks and blank space.

Lab write$-$up submission guidelines: You will submit your diary file lab$2.$txt online via Canvas

Assignments $.$ Lab write$-$ups will only be accepted if they are in plain text format or PDF format. A

lab writeup in any other format will not be graded!