- review linear transformations (p. 120)
- proof of rank-nullity theorem
- Know the relationship between left and right inverse and injective and surjective maps (as I did in class, not how the book did it).
- proof of theorem 4.8 (p. 127)
- practice test, problem 3b
- matrix representations of linear transformations (p. 132)
- It is a very good idea to get some practice with matrices for f using different bases, because I will give you a question about it on your exam.
- practice using formulae for finding the i, j entry in the product AB of two matrices & be able to prove basic things about these formulae
- be able to show that (AB)'=B'A', where C' denotes the transpose of C.
- know how to prove that the matrix product operation is associative
- Gaussian elimination
- spotting free variables and bound variables
- determine the kernal of a map using Gaussian elimination
- finding the inverse of a matrix
- prove
- if a matrix has a 0 row, the determinant is 0
- if a matrix has two rows the same, its determinant is 0
- more generally, if the rows are dependent, the determinant is 0
- if you interchange two rows, the determinant gets multiplied by -1
- review multilinearity (p.170)
- prove that the determinant of the inverse of a matrix is the reciprocal of the determinant of that matrix (using product formula)
- show that an n x n matrix is singular if and only if its determinant is 0 (using product formula)
- permutations
apr 8 2009 ∞
apr 10 2009 +
apr 10 2009 +