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In this video, we begin Chapter 1: Vector Spaces from the standard textbook Linear Algebra by Friedberg, Insel, and Spence. This lecture focuses on the geometric and physical motivation of vectors, including: Meaning of vectors (magnitude and direction) Vector addition and the parallelogram law Algebraic representation of vectors using coordinates Scalar multiplication and parallel vectors Fundamental algebraic properties of vectors Vector equations of a line and a plane in space The lecture is designed in a clear, exam-oriented manner, suitable for: CSIR NET (Mathematical Sciences) HPSET / State SET Assistant Professor preparation MSc / PhD coursework in Linear Algebra 📌 Exercises: At the end of the video, exercises from the textbook are provided for self-practice. 👉 Solutions will be discussed in the next video. 📚 Reference Book Friedberg, Insel & Spence – Linear Algebra ▶️ Next Video Lecture 2: Formal Definition of Vector Space 👍 If this video helps you Like the video Share it with fellow aspirants Subscribe for the full Linear Algebra (Friedberg-based) series 🔖 Tags / Keywords Linear Algebra Vector Spaces Friedberg Linear Algebra CSIR NET Mathematics HPSET Mathematics Assistant Professor Maths Vector Addition Scalar Multiplication Equation of Line and Plane