Questions and Answers
What is a vector?
What is the initial point or tail in vector AB?
point A
What is the terminal point or head in vector AB?
point B
The zero vector is denoted by 0.
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What is R2 in the context of vectors?
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What is standard position for a vector?
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U + V = [u1 + v1, u2 + v2] describes what?
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Cv = c[v1, v2] = [cv1, cv2] represents which operation?
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If c > 0, what does c represent?
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Study Notes
Key Definitions in Linear Algebra
- Vector: A directed line segment representing displacement from point A (initial point) to point B (terminal point).
- Initial Point (Tail): In the notation AB, point A is known as the initial point or tail.
- Terminal Point (Head): In the notation AB, point B is classified as the terminal point or head.
- Zero Vector: Indicates no movement or direction, represented by the symbol 0.
- R²: Refers to the set of all vectors that comprise two components, denoting a two-dimensional space.
- Standard Position: A vector is in standard position if its tail is located at the origin (point O).
Vector Operations
- Vector Addition: Denoted as U + V = [u1 + v1, u2 + v2], combines two vectors by adding their corresponding components.
- Scalar Multiplication: Represented by cv = c[v1, v2] = [cv1, cv2], this operation scales a vector by multiplying each component by a scalar value c.
Scalar Notation
- Scalar Characteristics: The context of c > 0 suggests that scalars can be positive, influencing the direction and magnitude of the resulting vector after multiplication.
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Description
Test your knowledge with these linear algebra flashcards covering key concepts such as vectors, initial and terminal points, and more. Perfect for students looking to strengthen their understanding of the subject. Review definitions and terminology essential for mastering linear algebra.
