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Definition Of Linear Equation
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Linear algebra is a foundation course for students entering mathematics, engineering, and computer science, and the fourth edition includes more problems connected directly with applications to these majors. It is also updated throughout to include new essential appendices in algebraic systems, polynomials, and matrix applications.
I am using this book as a review to supplement more advanced texts. I find it useful; for one thing, definitions are elaborated on; eg, consider the definition of linear dependence and independence: what if one of the vectors is 0? After all, the zero vector is still a vector. What if one of the vectors is a multiple of some other vector? What if the vectors in the basis are rearranged, etc? These are supposed to be elementary but we often need to be refreshed. Also, we may hastily read a definition and miss subtle points. This book points out some of the subtleties and helps clarify some of the theory even for math graduates.
This book's appeal is that it outlines Linear Algebra using a series of solved problems. However, when you actually sit down and do them, you find that many of them are just flat out wrong. It is quite frustrating when it asks you to prove something is linearly independent only to find out after 20 min of confusion that the vectors they gave you are actually dependent and you weren't wrong in the first place. Even their fully solved and explained problems have errors that could really confuse someone who was learning this topic for the first time.
I found this book to be very helpful.
Pros: Excellent as a supplement or even as a text. Lots of worked out problems, some are even proofs of theorms. The explanations are to the point and easy to understand. Good for math, physics or engineering undergrad majors. There is enough material for 1.5 undergrad semesters of Linear Algebra. Very appropriate for math GRE subject test review.
Cons: none
This book does not have the abstract algebra style, so not for math graduate school.
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