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The present book titled New College Algebra B.A./B.Sc. I, is according to the latest syllabus of First Semester students of K.U and M.D.U. It also caters to the needs of those students who want to have a sound understanding of the topics contained in this book for various competitive and other examinations. The contents of the book are as follows : 1. Matrices 2. Rank of a Matrix 3. Characteristic Equation of a Matrix 4. Applications of Matrices to a System of Linear Equations 5. Orthogonal and Unitary Matrices 6. Bilinear and Quadratic Forms 7. Relation Between the Roots and Coefficients of an Equation 8. Transformation of Equations 9. Solution of Cubic and Biquadratic Equations 10. Descarte's Rule of Signs