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