You can also stop by to see either Tom or Andy during their office hours (Monday 1:30-3 and 4-5, Wednesday 12-1:30 and Thursday 3:30-4:30) in their office, room 435 in the Science Center.

Also our Head CA, Mat Sapak, will hold a number of office hours in Loker next week:
     Monday 4:30-5:30, Tuesday 3-4 and Wednesday 6-8pm

Finally, don't forget to go to your CA's weekly problem session on Monday or Tuesday!!

...and remember  to take advantage of the Math Question Center which meets from Sunday to Thursday from 8 to 10 pm in Loker.

Topics for first midterm:

• Linear Systems:
• Setting up systems algebraically (translating written descriptions into systems of equations)
• Forms of systems - vector, matrix forms
• definition/use of coefficient matrix, augmented matrix
• Solving systems using row reduction (Gauss-Jordan elimination)
• checking if a matrix is in rref
• Geometric interpretation of solution sets (intersections of lines, planes, etc., number of solutions)
• Definition of rank of a matrix, relationship of rank, rref to number of solutions
• inconsistent (rank < # columns and at least one row in rref is 0...0 1)
• consistent - unique, infinite number of solutions
• Linear Transformations:
• Definition:  T(x) = Ax (where A is an m by n matrix, x is an n by 1 column vector)
• columns of A are images of standard basis vectors under T
• Main property of linear transformations - preservation of linear combinations of vectors
• Identification of basic types of planar transformations
• rotations (fact 2.2.2)
• reflections
• projections (including definition in fact 2.2.5)
• Skip shears
• Inverses of transformations - existence for a given transformation
• Matrices:
• Basic definitions (square, identity, dimensions given as row by column)
• Inverses
• computing using rref(A | I), existence of (only for n by n, if rank(A) = n)
• formula for inverse of 2x2 matrix, definition of determinant
• Matrix multiplication, addition
• how to compute products
• relationship to composition of transformations
• Properties of matrix multiplication, addition
• noncommutativity of product, distribution, associativity
• (AB)^-1 = B^-1A^-1
• Skip multiplying partitioned matrices
• Image and Kernel of a transformation
• Image = span of column vectors of transformation's matrix
• Kernel = zeros of transformation
• finding kernel subset using rref as before
• Properties of kernel, image subsets
• contain zero vector, closed under addition, scalar multiplication
• Note there are a couple of topics in the textbook that we did not cover in class, and which  will not be covered on the midterm:
• No shears (in section 2.2)
• No multiplying partitioned matrices (in section 2.4)

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Old Exams for practise:

• Note that although the class is similar from  year to year, there are differences in terms of the timing of  what was covered during the semester and when the first midterm is held.  For instance on the fall 1999 mid-term, you don't need to know how to do #4 part c at this point since we won't be testing on bases at this point this fall.  In addition to using the following practice tests, you should go through your old homework problems - they will give you a good sense as well of what you need to know for this semester's midterms.
• We will keep posting solutions to these exams, but do be sure to try to do them first on your own!
• Midterm 1 Fall 2001  (skip #1, 4, 6 for part a, just use the standard basis as the answer)  (Solutions)
• Midterm 1 Fall 2000  (skip #3)  (Solutions (.pdf format)) (.doc format)
• Midterm 1 Fall 1999  (skip #4 part c)  (Solutions)

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Textbook  True/False chapter review problems:

• Another good way to get ready for the midterm is to do the true/false review problems at the end of each chapter that we've covered.  We will post the answers to these true/false problems at some point soon.
• Note that a few problems (such as #47 in true/false for chapter 2) are on topics we have specifically excluded from the midterm (see list of such topics above), so there are a couple of problems that you shouldn't expect to be able to do - you should be able to figure out which ones these are by checking the list of topics covered/not covered.
• Answers to Chapter 1 True/False questions
• Answers to Chapter 2 True/False questions