Wed Nov 21 Update & Next HW assignement

We reviewed the cofactor expansion for computing determinants (Sec 3.1), and pointed out the special case for triangular matrices. We also talked through exercises 19-24, which indicate how the elementary row operations affect the value of the determinant.

That led into Sec 3.2, which outlines an easier way to compute determinants, via row reducing to echelon form. This in turn leads to a central result of linear algebra, which gives us another clause to add to the Invertible Matrix Theorem (recall Sec 2.3):

  • a square matrix A is invertible if and only if det A is non-zero

See below for the homework exercises to do for these two sections, due next Monday–also posted on the HW Assignments page (always accessible via the header above).

We’ll pick up with some additional stuff in Sec 3.2 on Monday, and then move ahead to Ch 5 (Eigenvectors & Eigenvalues).

HW due Monday November 26:

  • Sec 3.1 (Introduction to Determinants): #1-13 odd, 19-29 odd (30, 31, 41, 42, 43M, 44M, 46M)
  • Sec 3.2 (Properties of Determinants): #1-13 odd, 15-23 all
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Khan Academy: Linear Algebra

You may find the Khan Academy’s Linear Algebra videos helpful.  Here is the video for the topic we discussed in class on Monday:

Finding the determinant of a 3×3 matrix

See also the videos for nxn determinants, and for computing determinants along other rows/columns.

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Hello Math 2580/6653 World

Welcome to the OpenLab site for Math 2580/6653 – Introduction to Linear Algebra (Fall 2012). I’m going to belatedly start using OpenLab for course annoucements, posting documents & links, etc.

So please join the course (from the course profile page, which should then show up under “My Courses” under “My OpenLab”), and/or bookmark this blog site (and/or the course profile page).

Please check this blog as well as the course profile periodically, especially if you ever miss class.  I’ll try to post a summary of topics covered in class here, as well as update the pages with the HW assignments/schedule, additional readings, etc.  Also feel free to use the Discussion forum to post questions.


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