Linear Algebra: Vectors in Rn, Lecture notes of Linear Algebra

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MATH 301i – Linear Algebra

Instructor: Mohamed Abdou Mahran Kasem, Ph.D.

NU – EAS

Lecture code of ethics o Attendance is mandatory o No cell phones o No side talks o Write as much as you can

Lecture Contents ➢ Linear combinations ➢ Spanning set ➢ Linear independence ➢ Dot product

Vectors in a plane

• In physics and engineering, a vector is characterized by two quantities (length and direction) and is represented by a directed line segment.
• A vector in the plane is represented geometrically by a directed line segment whose initial point is the origin and whose terminal point is the point.
• This vector is represented by the same ordered pair used to represent its terminal point. That is,

Vectors in a plane

Example – 2

Vectors in a plane

Example – 3

Vectors in 𝑅 𝑛

Vectors in 𝑅 𝑛

Vectors in 𝑅 𝑛

Vectors in 𝑅 𝑛

Example – 2

Vectors in 𝑅 𝑛

Example – 3

Length and Dot Product in 𝑅 𝑛

Length and Dot Product in 𝑅 𝑛

Length and Dot Product in 𝑅 𝑛