Math 110, Spring 2014. Midterm Review
Things You Must Know:
Denitions:
Ch. 1 - vector space over F , subspace, sums of subspaces, direct sums of subspace (in particular,
they are special types of sums).
Ch. 2 - nite dimensional spaces, spanning lists, lin
Worksheet 1/22. Math 110, Spring 2014. Solutions
These problems are intended as supplementary material to the homework exercises and
will hopefully give you some more practice with actual examples. In particular, they may be
easier/harder than homework. S
Worksheet 3/5. Math 110, Spring 2014.
These problems are intended as supplementary material to the homework exercises and
will hopefully give you some more practice with actual examples. In particular, they may be
easier/harder than homework. Remember tha
Worksheet 2/5. Math 110, Spring 2014. Solutions
These problems are intended as supplementary material to the homework exercises and
will hopefully give you some more practice with actual examples. In particular, they may be
easier/harder than homework. Se
Worksheet 3/31. Math 110, Spring 2014. SOLUTIONS
These problems are intended as supplementary material to the homework exercises and
will hopefully give you some more practice with actual examples. In particular, they may be
easier/harder than homework. R
Worksheet 1/29. Math 110, Spring 2014.
These problems are intended as supplementary material to the homework exercises and
will hopefully give you some more practice with actual examples. In particular, they may be
easier/harder than homework. Send me an
Math 110, Spring 2014. Dual Spaces Review
Let V be a vector space (over F ). Recall that the dual space of V , denoted V , is the set
of all linear maps from V to the one dimensional vector space F :
V = cfw_T : V F | T is a linear map.
Also, in Axlers no
Math 110, Spring 2014. Solutions to HW1, 1.C Q8, Q12
8) EDIT: an easier example was outlined to me. I leabe my (very) involved example below.
Hopefully its of some use to someone.
Take f (x) = x to be
periodic with period 1 that f (0) = f (1) = 0), and g
Math 110, Spring 2014. Quotient Spaces Review
Let V be a vector space over F (recall that we always assume that F cfw_R, C) and U V
be a subspace.
We dene an ane subset of V parallel to U to be a subset of the form
def
v + U = cfw_v + u | u U
for some v V
Math 110, Fall 2013. Proof Tips
The following are some tips that may (or may not) beuseful when attempting to prove statements. Of course, approaching a proof is like xing a drink - there are many ways to make a
good margarita :)
Subspaces, Sums, Direct S
Prof. Ming Gu, 861 Evans, tel: 2-3145 Email: mgu@math.berkeley.edu http:/www.math.berkeley.edu/mgu/MA110F2011
Math110 Sample Midterm I, Fall 2011
This is a closed book exam; but everyone is allowed a standard one-page cheat sheet (on one-side only). You n
Prof. Ming Gu, 861 Evans, tel: 2-3145 Email: mgu@math.berkeley.edu http:/www.math.berkeley.edu/mgu/MA110F2011
Math110 Sample Final, Fall 2011
This is a closed book exam; but everyone is allowed a standard one-page cheat sheet (on one-side only). You need
Prof. Ming Gu, 861 Evans, tel: 2-3145 Email: mgu@math.berkeley.edu http:/www.math.berkeley.edu/mgu/MA110F2011
Math110 Sample Midterm II, Fall 2011
This is a closed book exam; but everyone is allowed a standard one-page cheat sheet (on one-side only). You
Prof. Ming Gu, 861 Evans, tel: 2-3145 Email: mgu@math.berkeley.edu http:/www.math.berkeley.edu/mgu/MA110F2011
Math110 Sample Midterm I, Fall 2011
This is a closed book exam; but everyone is allowed a standard one-page cheat sheet (on one-side only). You n
Worksheet 2/26. Math 110, Spring 2014. Solutions
These problems are intended as supplementary material to the homework exercises and
will hopefully give you some more practice with actual examples. In particular, they may be
easier/harder than homework. R