# Exam III tomorrow

Hi everyone, just wanted to holler and give you the rundown on tomorrow’s exam. It’ll cover all the material we’ve done since Exam II, which is the stuff from the lecture notes posted in the Documents tab, plus sections 4.2 and 5.3 from the textbook (mostly 5.3 pseudoinverse stuff). If you want to do well, you should know how to do all the problems from the homeworks and the practice problems, including:

– Proving that a vector x is or is not in the span of a set of vectors

– Definition of basis, linear dependence, span

– Finding the solution set of an underdetermined, consistent system

– Finding bases for row(A), col(A), null(A)
– Knowing rank(A), nullity(A)

– Proving a set S is a subspace (use the theorem by showing that S is the span of a set of vectors)
– Proving a set S is not a subspace (use a counterexample (with numbers) to show that S violates one of the requirements for being a subspace)

– Proving that T is a linear transformation (use the theorem by showing T is a matrix transformation)
– Proving that T is not a linear transformation (use a counterexample (with numbers) to show T violates one of the requirements for being linear)
– Knowing the domain, codomain, range of T

– Calculating best approximate solution of an overdetermined system by using the pseudoinverse

For the proofs and other analytical parts of the test, the most important things to understand are the rank theorem, the fundamental theorem of invertible matrices, and the fact that the matrix-vector equation Ax = b means that b is a linear combination of the columns of A, where the coefficients are the components of x

I think about truffle cheese a lot more than is probably normal. Now, you know I am a bit of a cheese nut so this probably comes as no great shock. (Side note: “cheese nuts”would be a great snack, right? Wait, would they? Would they just be gross? I guess I’d probably have to figure out what they are first. Maybe a nut that is embedded in some cheese. Probably not that great. Wait maybe then you fry it? Better, definitely. But good? I’m not sure. I feel like cheese and nuts, while each excellent on its own, ought not be mixed, kind of like Chinese food and cheese. I’ll have to spend some time in the lab and get back to you on this.) However, I believe that (abnormally large volume of cheese thoughts aside) my ratio of truffle cheese-related thoughts to non-truffle cheese-related thoughts is higher than the national average by statistically significant margin.

I think about a cheese called Truffle Tremor, which is made by Cypress Grove, of Midnight Moon and Humboldt Fog fame:

Midnight Moon is the goat gouda that you might recognize from a little store called Every Bodega In Williamsburg; Humboldt Fog is your momma’s favorite fancy cheese. They’re both actually pretty good, but snobs like me enjoy taking the piss out of people for enjoying them, then retreating to our dens of sadness to eat monk-crafted, limited-release, beer-washed smelly cheese while listening to our #veryrare vinyl of the Monkees’ Davy Jones strangling bats in a Lebanese cave.

Anyway, Truffle Tremor is basically Humboldt Fog minus the center ash line plus black truffles. It’s good because it tastes like cheese but it also tastes like truffles. Sounds simple enough. The problems arise in a truffle cheese when it overreaches. I bought a cheese at Trader Joe’s once that purported to be a truffle cheddar. The price was just \$6/lb, which should have given me pause (Truffle Tremor is \$35/lb at Murray’s, though I think only \$24 or so per lb (precut, though) at Union Market). What sort of truffles could they be using to keep the price point that low? As it turned out, there weren’t many truffles involved at all. There was truffle oil and truffle paste, but I felt them merely as truffle remnants, truffle shadows. Truffle memorie that linger only in imagined senses. In trying to be all things for all people — the common man’s reclamation of the princely food — this cheese betrayed itself. We all can learn a lesson from its failure — as Polonius advises, this above all else: to thine own self be true. If you are a \$6/lb cheese, be at peace with your nature. Do not cloak yourself in the vestments of a finer curd, but rather accept your limitations, and own them.

If you memorize the Norton Anthology of Poetry and a map of Africa, that’ll help with the extra credit on tomorrow’s exam.

If you memorize “You’ll Never Walk Alone” that’ll help win over the next Liverpool fan you meet.