Book for studying Linear Algebra

Question

So I'm taking Linear Algebra in college. However, I'm not getting the grades I want and I have sort of difficulties using my teacher's book: it has very formal explanations and a strong lack of examples. I'm looking for a book that has a good explanation of the content and also solved exercises (which is a very important thing that I'm missing). So here is a list of books my college has:

Calculus: T. M. Apostol 1994 Vol. I. and Vol.II Reverté

Linear Algebra and Its Applications: G. Strang 1988 3rd ed. Academic Press

Linear Algebra: S. Lipschutz 1994 Schaum's Outline Series. McGraw-Hill

What is in your opinion the best book for self-study? (I'm going to repeat the examinations next semester but I'll be studying on my own.) If there is a better book than the ones on this list please tell me. Thanks!!

EDIT: I study in a Portuguese-speaking country and we use a Portuguese book.

The contents of the course are:

Systems of linear equations. Gaussian elimination. Vectors and matrices. Inverse matrices. Linear spaces and linear transformations. Linear independence, bases and dimension. Kernel and range of a linear transformation. Applications to linear differential equations. Inner products and norms, orthogonal bases and Gram-Schmidt orthogonalization, orthogonal complements and projection onto subspaces. Applications to equations of straight lines and planes. Least squares approximations. Determinants and their applications. Eigenvalues and eigenvectors. Invariant subspaces. Diagonalization of matrices. Jordan forms. Hermitian, skew Hermitian, and unitary transformations. Quadratic forms.

Answer 1

For my undergraduate linear algebra course, I used Friedberg's book, 4th ed. http://www.amazon.com/Linear-Algebra-4th-Stephen-Friedberg/dp/0130084514/ref=sr_1_1?ie=UTF8&qid=1452808996&sr=8-1&keywords=friedberg+linear+algebra

This book will cover both the technical and abstract concepts of linear algebra while also providing many different types of examples and applications of linear algebra. These will include all the concepts you have listed and there are plenty more topics should you be interested.

A potential drawback of the book is that it is geared for the more mathematically-leaning student. There will be proofs and you will build linear algebra in a more axiomatic fashion. Of course the advantage of this is that matrices are no longer ad hoc. It will describe and prove explicitly how one obtains a bijective correspondence between matrices and linear functions between finite dimensional vector spaces upon fixing a basis.

Answer 2

I can heartily recommend Linear Algebra, as I am the author. Coverage is what you asked for, with an emphasis on improving students's mathematical maturity, including lots of examples using computations. It is totally Free and you can also get a physical book from Amazon if you prefer that. There are completely solved answers for all exercises, on the web page (click on the question for the answer and click on the answer for the question). In addition, the beamer slides do different examples from the book, so that's twice as many examples right there.

Answer 3

I find an old book

A.I. Kostrikin, Yu.I. Manin, Linear algebra and geometry. Translated from the second Russian edition by M. E. Alferieff. Algebra, Logic and Applications, 1. Gordon and Breach Science Publishers, New York, 1989. x+309 pp.

quite readable. It appears to match the contents of your course (and goes beyond it) and, as far as I recall, has a fair share of examples.