In this post, we will see the book from the series Little Mathematics Library titled Systems of Linear Equations by L. A. Skornyakov.

About the book

The book contains a complete exposition of the theory of systems of linear equations employing only elementary operations on matrices. The method of complete mathematical induction is, formally, not used here. However, in some cases it is hidden behind the words “etc.”. Each section is followed by exercises. The main purpose of the exercises is to give the reader an opportunity to test his mastery of the material. The book is intended for a wide circle of readers, including pupils of senior classes of secondary schools, who are interested in mathematics.

The book was translated from Russian by Eugene Yankovsky and was published in 1988 by Mir.

A big thank you to @4evercla6 for this and two more books from LML series. See the comment in the LML taking stock post. We will see them in the next couple of posts.

Now only The Euler Characteristic by Yu. A. Shaskin remains from the list!

You can get the book here.

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Contents

Preface 6

1. Systems of Linear Equations and Their Solutions 7
2. Matrices and Their Elementary Transformations 11
3. A Method for Solving Systems of Linear Equations 22
4. The Rank of a Matrix 31
5. The Theorem on Principal Unknowns 39
6. Fundamental Systems of Solutions 48

Answers 56
Solutions 60