Practice makes perfect! At least as they say…These are some interesting problems found and made, maybe you’ll like doing them? Anyhow, the date it’s due is June 12, 2021, book it! If you are stuck, try office hours, google, peers, and the book or notes!
Question 1
Given a matrix such as
\[M = \pmatrix{a & b \\ c & d}\]Why does the set the entries belong to determine the row space? column space? Write up the values of $a, b, c, $ and $d$ so that the row space and column space are the same. This is known as invariance under transposition.
Question 2
Your lab partner measured the amount of CO2 in each bottle of soda one by one 100 times as part of a science quality control experiement. Unfortunatly, they aren’t too keen on analysis of these numbers. How can you tell if the roughly the same amount of CO2 is present from this sample? What might be your initial hypothesis?
(and so on..)