A Level and Further Maths

A matrix is more than a grid of numbers. It moves the plane.

This prototype helps learners see 2 by 2 matrices as transformations: stretching, shearing, rotating, reflecting and sometimes collapsing area.

The aim is to connect the algebra of matrix multiplication with the geometry of vectors, shapes, determinant and orientation.

Transformation lab

Watch a matrix move points, vectors and area

A 2 by 2 matrix transforms every point in the plane. The columns of the matrix show where the basis vectors go, and the determinant shows what happens to area.

Determinant

0.8

Area scale

0.8

Orientation

preserved

Basis images

(1, 0.25) and (0.8, 1)

Joy in the process

The point is not just to finish. It is to notice, test and return.

These tools are invitations to explore. A good mistake, a surprising pattern or a question you cannot yet answer is part of the work, not a failure of it.

The challenge is deliberate: the site should support thinking, not remove the need for it.

Before changing a setting, pause and predict what you think will happen.

Change one thing at a time. What stayed the same, and what changed?

Try to create a surprising case, a broken case, or a beautiful pattern.

Ask what this connects to outside the page: maps, movement, nature, systems or decisions.

Reset, then try again with a new question in mind.

Future extensions

This can grow into a full linear algebra playground.

Add eigenvector highlighting as directions that stay on the same line.

Add animated interpolation from the identity matrix to the chosen matrix.

Add challenge tasks for rotations, reflections, shears and singular matrices.

Add side-by-side algebra showing how each point is transformed.