If you're joining the class late, please print and fill this out and give it to me in class.

Name:

Year and (intended) major:

What times would you most like an office hour? (Give at least four possibilities -- keep in mind I have another class right before this one.)

For each statement or concept following, indicate your level of familiarity with it. (Even the false statements may be familiar...) Basically I'm expecting most check marks in the last two columns.

	Old hat	Somewhat familiar	Heard of it	No clue here
"Linear transformations correspond 1:1 to matrices"	.	.	.	.
"Every real vector space is isomorphic to R to the n, for some n"	.	.	.	.
"Let T:V to V, C a cube in V of volume 1. Then volume(T*C) = | det T |."	.	.	.	.
Jordan canonical form	.	.	.	.
vector spaces over {0,1} with 1+1=0	.	.	.	.
"Hermitian matrices have real eigenvalues and are diagonalizable"	.	.	.	.
the quotient space V/W of a vector space V by a subspace W	.	.	.	.
"The projective plane is the affine plane plus the line at infinity"	.	.	.	.
"Row vectors are naturally dual to column vectors"	.	.	.	.
the quaternions {a+bi+cj+dk : a,b,c,d real}	.	.	.	.

Recall that the transpose M^T of a matrix is defined by "M^T's i,j entry is M's j,i entry".

Let A be the 3x2 matrix

2 5 -1 3 0 -1

and B the 3x2 matrix

-1 0 2 3 1 1

so A^T =

2 -1 0 5 3 -1

Show your work in the following (on the back of the sheet if need be):

1. What is det (A^T * B)?

2. What is det (A * B)?

3. What is det (A * B^T)?

Anything else I should know about your mathematical background?