Pre Linear Algebra (Pbi. U.)

The book is strictly in accordance with the latest syllabus of the PUNJABI UNIVERSITY, PATIALA. The entire subject matter has been arranged in a systematic, graded, simple, lucid and exhaustive manner. Each chapter begins with some definitions followed by theorems with complete proofs and solved problems. A large number of notes and remarks have been added for a better understanding of the subject. Well-planned and exhaustive exercises have been given in each chapter.

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Elementary operation on matrices. Inverse of a matrix using Gauss Jordan Method. Linear independence of row and column vectors, Row rank, Column rank and their equivalence. Eigen values, Eigen vectors and the characteristic equation of a matrix, Diagonalization, Cayley-Hamilton theorem. Consistency of a system of linear equations.

       Vector spaces, Examples, Linear Dependence, Linear Combinations, Bases and Dimension, Subspaces, Linear transformation, Algebra of linear transformations, Matrices as linear transformations, Matrices and change of basis, Kernel and image, Rank and Nullity theorem.

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