Last changed: December 14, 2001.
The course meets 5 times a week: Lectures, 10:10am-10:00am MWF in Nicholson
Hall 216, (Max Jodeit, VinH 258, 5-3855, jodeit@math.umn.edu)
and
Discussion sessions at 10:10 in Norris 3 or 12:20 in MechE 18, depending on
section; your TA is Kijung Lee (www.math.umn.edu/~kjlee/2573h.html).
The TEXTS are
Multivariable Mathematics, by Richard E. Williamson
& Hale F. Trotter,
and
Linear Algebra with Applications, 2nd ed,
by Otto Bretscher
Max Jodeit's Office Hours: 1:30 - 2:15 MWF, Otherwise, by appointment -- or call 5-3855 to see if I'm in and available.
Links, if any, to other Web pages or documents related to this course will go here. Announcements, hints, "news" will also be here.
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An express tour thru determinants. Version 3a, 17 pages
projection-matrix formulas, review of Gram-Schmidt-2573H...
Two rref's are equal iffi their kernels are equal
We will cover pp 1-38 quickly (examples pp 9-17 have the essence of the Gauss-Jordan method of elimination). We have these goals:
* learn how to reduce a linear system to one that is "upper triangular"
* learn how to reduce an upper triangular system to a "diagonal" one
* learn how to interpret our results in "matrix operation" ways
* learn about kernels, images, and bases for them
* learn how to tell how many solutions a system of linear equations has and how to express them in a simple way
Elementary Row Operations and ERO matrices are discussed on pp 87-88,
Exercises #50 -- 56.
Section 2.3 covers invertible matrices: Def 2.3.2, example of
( A | I ) -> ( I | A^{-1} ) on page 68.
When this cannot be done ( A not invertible ) we get
( A | I ) -> ( rref | M ) and MA = rref checks that we made no
(net!) mistakes.
The formula for the ij entry of a product of two matrices is on page
78. Why does Bretscher work with BA insread of AB?
Fact 2.4.9 depends on finite dimension! The Right and Left
shift operators furnish a counterexample in the infinite-dimensional case.
Partitioned matrices, or "matrices in block form" are discussed on page 82.
Section 3.1 covers kernels and images.