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The approach is developmental. Although it covers the requisite material by proving things, it does not assume that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise each student's level of mathematical maturity.
From the Author: For a quick look, I suggest the second chapter. The first chapter is necessarily computational but the second chapter shows more clearly what the book works on: bridging between lower-division mathematics with its reliance on explicitly-given algorithms, and upper division college mathematics with its emphasis on concepts and proof.
Title: Linear Algebra
Publisher: Orthogonal Publishing L3C
Publication Date: 2017
Binding: Paperback
Condition: Very Good
Edition: 3rd Edition