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This book is an INTRODUCTION TO LINEAR ALGEBRA VOL -1 for graduate and under graduate students. The basic idea of linear algebra along with the many examples is discussed in this book. This book provides a thorough knowledge of matrix, vector space, linear transformation, inner product space, Dual space and eigenvalues & eigenvectors. It also helps to the reader in solving different kinds of problems in linear algebra. This book possesses four chapter. Also at the of every chapters, multiple objective questions are discussed.