Learning path · Introductory linear algebra
Linear algebra foundations
Build from equations and coordinates to vectors and matrices. Explain what each component represents and how a matrix-vector calculation combines quantities.
4 units · 6 skills
Starting point: Introductory linear algebra
For learners comfortable with basic equation work and ready to use coordinates, vectors, and matrices. Calculus is not a prerequisite for the mathematics introduced in this path.
What this path connects
- Connect a system of equations to a shared solution.
- Calculate and interpret a linear combination of vectors.
- Read matrix dimensions and evaluate a matrix-vector product.
The learning sequence
See what each unit covers and open the skill you want to understand. The order gives you a route through the material.
Unit 1
Use signs and coordinates reliably
Review component signs and coordinate order so the geometry and calculation describe the same movement or relationship.
- Signed numbersUse a number line to make sense of positive and negative numbers. Distinguish a value’s position from its distance from zero and explain changes in either direction.
- Graphs & coordinatesRead a graph as a relationship between quantities. Check axes and scale, connect points to an equation, and interpret the change between two points.
Unit 2
Satisfy more than one equation
Connect single-equation reasoning to a system, and check each proposed value against every relationship.
- Linear equationsSolve a one-variable linear equation with justified steps. Keep both sides equal and check the solution in the original relationship.
- Systems of equationsSolve two linear equations together using their shared variables. Connect elimination or substitution to the intersection of the corresponding relationships.
Unit 3
Combine quantities as vectors
Use corresponding components to add vectors and scale them. Interpret a linear combination in a coordinate picture.
Unit 4
Organize the operation with a matrix
Check dimensions and compute a row-by-column product. Connect the output to the coefficients or transformation represented by the matrix.
Make the path useful to you
Separate conceptual and enrollment prerequisites
An institution may require other courses before enrollment. The algebra and coordinate ideas here do not require calculus; consult the relevant syllabus when preparing for a formal course.
Keep the dimensions visible
Write the shape of a matrix or vector before multiplying. This catches an invalid operation and helps explain the type of output you should expect.
Use these foundations for later study
A fuller course develops spaces, independence, bases, determinants, eigenvalues, projections, and further applications. These introductory skills provide a starting point for those topics without claiming that the whole course is covered.
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