$(20$ points$)$ Write an $R$ script for parts $($a$),($b$)$ and $($c$).($see next page$)$

Run the script and hand in your $R$ execution results.

Include the $R$ commands in your $HW1R$ script file submitted in canvas.

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Homework: Module $1$

$($a$)$ Create a matrix A with $25$ rows, $2$ columns, and all entries equal $1.$

$($b$)$ Reassign the first column of $A$ so that the entry in the $k$ th row and first column is: $2k.$ That is$,$ the $($row $k,$ column $1)-$entry of $A$ is reassigned to $2k$ for $k=1,2,3,$cdots,$25.$

$($c$)$ Using a for $()$ loop, reassign the entries of the second column of $A$ as follows:

For odd $k,$ reassign row $k,$ column $2$ of $A$ as: $\sqrt[\phantom{2}]{k}.$

For even $k,$ reassign row $k,$ column $2$ of $A$ as: ${\displaystyle \underset{e}{\overset{k}{}}}logtdt.$

This is the log with base $e=$exp$(1).$ You may want to use $value at the end of the line.