Linear algebra
Linear algebra: 18 free interactive math resources. Systems of equations, the coordinate plane, and linear maps — visual first steps.
Guide
About this topic
Linear algebra intro uses systems graphs and the plane — intersection as solution — before matrices and vectors.
What you learn
- Graphical solutions of linear systems
- Early vector intuition on the plane
- From intersection back to elimination
- Write matrices in the editor
Subtopics
Key formulas
ax + by = cmatrix notation
FAQ
Do I need matrices first?
No — understand systems graphically, then add matrix language.
Link to algebra/functions?
Shared linear/coordinate tools; stress geometric meaning of solutions.
How do I type a matrix?
Use matrix templates in the equation editor library.
Resources in this topic
18 free interactive resources in 4 groups
Number line & absolute value
Equations & inequalities
- Activity
Properties of equality (balance)
A balance model for adding/subtracting/multiplying/dividing both sides to isolate x.
Open - Activity
Linear inequalities in one variable
Show solution sets of ax + b ? 0 on the number line.
Open - Activity
Systems of two linear equations
The intersection of two lines is the solution of the system.
Guide - Activity
Systems of linear inequalities
Intersection of two half-planes — the green region is the solution set.
Guide
Polynomials & factoring
Functions as algebra
- Activity
Linear function y = kx + b
Adjust k and b to see slope and vertical shift of the line.
Guide - Activity
Linear intercepts
Find axis intercepts and the triangle they form with the origin.
Open - Activity
Quadratic y = ax² + bx + c
Adjust a, b, c to see opening, axis of symmetry, and vertex.
Guide - Activity
Vertex form of a parabola
From y = a(x − h)² + k, see how translations move the parabola.
Guide - Activity
Inverse variation y = k/x
Vary k to see the hyperbola branches and asymptotes.
Guide - Activity
Maximum area under a parabola
P moves on a parabola; maximize area of △PAB (vertical height).
Open - Activity
Exam functions: hyperbola vs line
Compare k/x and a line through two points; read inequality solution sets.
Open - Activity
Coordinate plane intro
Quadrants, coordinates, and where a point sits.
Guide - Activity
Plane vector operations
Vector addition (parallelogram rule) and scalar multiplication.
Open