The book contains five sections: the matrices and determinants and county and remittances destined written and linear equations and also the distinctive values and vector and distinctive, and the book aims to present the principles of reparation linear level that makes it a good book to be the curriculum for university students from athletes and Veziaeein, engineers, and be a reference for students of universities and higher institutes after listing applications written reparation matrices in general and especially in the different branches of science such eventualities, insurance and the economy.