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Multiplying a matrix by a column vector | Matrices | Precalculus | Khan Academy
Vectors | Chapter 1, Essence of linear algebra
Matrix multiplication as composition | Chapter 4, Essence of linear algebra
[Linear Algebra] Adding and Multiplying Vectors
Dot products and duality | Chapter 9, Essence of linear algebra
Matrix-vector and Matrix-matrix Multiplication
Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra
Cross products | Chapter 10, Essence of linear algebra
Scalar Multiplication of Vectors
3. Multiplication and Inverse Matrices
Matrix-Vector Multiplication Example
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Last Updated: October 16, 2026
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We learned how to add and subtract Practice this lesson yourself on KhanAcademy.org right now: ... Why the formula for dot products matches their geometric intuition. Help fund future projects: ... This videos gives two interpretations of The fundamental concepts of span, This covers the main geometric intuition behind the 2d and 3d cross products. Help fund future projects: ... This video discusses the scalar Learning Objectives: 1) Verify that