#import "@local/evan:1.0.0":*

= Solutions to Part Bravo

== Solution to @exer-basis-birthday

Neither vector is zero,
and for almost everyone the two vectors won't be a multiple of each other.
So for most people the answer is that the span is *all of $RR^2$*.

In order to find a K-pop idol whose two vectors are linearly dependent
(to get the answer "line" instead),
we need to find a database of K-pop birthdays, and we need to know where to look in it.
There are roughly two strategies you can adopt:

- For idols born before 2000, the only year that's viable is 1995
  (because $19$ is a prime greater than $12$, the last two digits need to be a multiple of $19$).
  The two days that work here are January 5 and February 10.
  As an example, <NAME> from former boy group Snuper was born on February 10, 1995.

- For idols born after 2000, good years to try would be 2004 or 2005.
  (The year 2004 has May 1 and October 2; the year 2005 has April 1, October 2, December 3.)
  As an example, <NAME> from KJRGL was born on October 2, 2004.
