The answers to zhanghua's mathematics translation can be downloaded from the website of educational materials. This book is a new modern textbook, which gives a new basic introduction to linear algebra and some interesting applications. The purpose is to help students master the basic concepts and application skills of linear algebra, and lay a foundation for the study and work practice of subsequent courses. The main contents include linear equations, matrix algebra, determinant, vector space, eigenvalue and eigenvector, orthogonality and least square method, symmetric matrix and quadratic form, vector space geometry and so on.