Reading list chapter 3
Read: Schaum chapter 3, without ‘Application to Systems of Linear Equations’ of section 3.13.
A note on augmented matrices (e.g., matrix M in pg. 59): a common practice when using augmented matrices is to draw a vertical line that separates the coefficients from the constants (this does not affect the computation). Though this is not always used in Schaum’s book, you might find it more convenient. See examples in the “no bullshit” book (3.1 Computational linear algebra: pg. 145 – augmented matrix) or this Wikipedia page: https://en.wikipedia.org/wiki/Augmented_matrix.
A note on sections 3.7-3.8: if you are struggling with understanding the procedures used offered in these sections for obtaining echelon and canonical matrices, then try to first read NBGLA book: section 3.1: pg. 144-150. Note that the term “reduced row echelon form (RREF)”, introduced in the NBGLA book, is equivalent to the “row canonical form”, introduced in Schaum’s book.
A note on section 3.9: you might also find NBGLA book: section 3.2 Matrix equations: pg. 157 helpful.
Note a typo: in pg. 65, section 3.5: ‘Systems in
Triangular and Echelon Forms’, remark –
the second equation should have been: 5x2-x3=-11
Note a typo: in pg. 71, example 3.10, the matrix on the left, the zero coefficient m2,3 should not have been circled (as a zero coefficient cannot serve as a pivot).
Note a typo: in pg. 87, section 3.12, DEFINITION – it should have been theorem 3.21 (rather than 3.18).
Relevant exercises: without 3.16, 3.19 (you may only read the corresponding answers), without 3.34. Important (theorems): 3.5, 3.10, 3.34, 3.36, 3.38, 3.45
Resources: (you might want to increase the speed when viewing the videos)