The student is asked to enter a given matrix, but they're only required to fill in the upper triangle.

A custom marking algorithm fills in any empty cells in the lower triangle of the student's answer with the corresponding cell in the upper triangle.

The student is still warned if they leave any cells empty in the upper triangle.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

The CSS preamble adds a vertical line down the input for part b, to separate the two parts of the matrix.

Calculate the magnitude of a 3-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v_1\\v_2\\v_3}$.

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

Example of an explore mode question. Student is given a 3x3 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)

Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Cofactors Determinant and inverse of a 3x3 matrix.

Exercises on calculating the determinant of 2x2 and 3x3 matrices.

Exercises on calculating the determinant of 3x3 matrices.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

This question tests learner's knowledge of the inverse matrix method for a 3x3 matrix.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

This exam gives an overview of skills studnets require to be able to add and subtract matrices.

This exam gives tests for an overview of the skills students need to be able to perfom matrix multiplications.

Multiplication of two matrices.

This is a collection of questions to test different aspect to consider when representing a matrix.

This question tests understanding of subscript notation for matrices

A demo of the matrix entry part and its options.

A few questions which show off the new matrix entry part.

Find principal stresses by finding the eigenvalues of the matrix

The student is shown one graph, and asked to type the adjacency matrix

Alternative version of Graphs: Match graph to its adjacency matrix, where the student must match an adjacency matrix to a graph.

This shows one way of laying out matrix cells in a table, so that some cells can be filled in by the student.

At the time this was written, there's an open issue for allowing some entries in the matrix entry part to be filled-in, which would make this technique redundant.

Some CSS in the preamble adds the brackets around the table - it has to have the attribute class="matrix-gaps"