Represent several components as one vector and explain addition or scaling. Connect component calculations to direction, size, and a coordinate picture.
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Linear algebra
Start with vectors, matrices, and systems of equations. Learn what the notation represents and how linear combinations connect calculations to a geometric picture.
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Explore linear algebra
Read a matrix by its rows and columns and calculate a matrix-vector product. Connect the result to coefficients, linear combinations, or a transformation.
What you’ll learn
- Interpret vector components and form a linear combination.
- Organize a calculation using a matrix.
- Connect a matrix-vector product to a system or transformation.
Work with several quantities together
A vector groups components that belong to one mathematical object. A matrix organizes coefficients or describes a linear transformation. Their shapes and dimensions tell you which operations make sense.
Systems provide a familiar starting point
A system of linear equations asks which values satisfy several relationships together. Vector and matrix notation helps express that question compactly and prepares for larger systems.
Preparation is about the ideas, not a universal course order
Algebra and coordinates are useful foundations. Calculus is not mathematically required for introductory linear algebra, although a university may set its own enrollment prerequisites. This catalogue begins with vectors and matrices; later study can add spaces, bases, and eigenvalues.
Keep exploring
VectorsRepresent several components as one vector and explain addition or scaling. Connect component calculations to direction, size, and a coordinate picture.MatricesRead a matrix by its rows and columns and calculate a matrix-vector product. Connect the result to coefficients, linear combinations, or a transformation.Systems of equationsSolve two linear equations together using their shared variables. Connect elimination or substitution to the intersection of the corresponding relationships.
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