Today, in class, I answered some homework questions from Section 1.4, including the following problems: Show that an upper triangular matrix with non-zero diagonal entries is nonsingular. (We’ve not covered determinants yet so we used a row-equivalence to the Identity argument) Show that the inverse of an upper triangular matrix is upper triangular. (We used… [Read more…]
February 13, 2007
In class today, we finished the section on partitioning matrices. We verified that that block matrices obey the same rules for matrix algebra. In particular, block matrix multiplication works as scalar multiplication as long as the dimensions are appropriate for the sub-matrices to be multiplied together. We looked at a couple of examples how we… [Read more…]
February 12, 2007
On Wednesday, last week, we completed our material over elementary matrices, using them to derive the inverse of a matrix. Upon proving that a matrix is non-singular (i.e., invertible) if and only if it is row equivalent to the identity, we noticed that the same row operations that change a matrix A into the identity… [Read more…]
February 5, 2007
I don’t think it is possible for me to cover a whole section of this linear algebra book in one class. Today, we started the section on Elementary Matrices and just a little ways in, I knew it was going to be a difficult section. The main purpose of this section is to use the… [Read more…]
January 31, 2007
It took three classes but I finally finished all of the section over matrix algebra. During today’s lecture we walked through the concepts of matrix inverse and matrix transposes. It’s amazing how long these lectures stretch out when you choose to demonstrate the concepts with examples involving matrix operations. As far as I can tell,… [Read more…]
January 30, 2007
During Linear Algebra on Monday, I began class by answering homework questions. I clarified the fact that [tex](0, \alpha, -\alpha)[/tex] and [tex](0, -\alpha, \alpha)[/tex] represent the same general solution to a linear system when [tex]\alpha \in \mathbb{R}[/tex]. Somehow the discussion of applications of the techniques we are learning came up. Thus far, we have basically… [Read more…]
February 18, 2007
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