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

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

This question tests students knowledge of basic matrix arithmetic.

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

Calculate the magnitude of a 2-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v1\\v2}$.

(a) Read subscript notation to identify an element in a 3x3 matrix; (b) chose the correct subscripted name from a list for a given element in a 3x3 matrix.

Find the determinant of  a random (3x3) matrix.

Find the determinant of a random (2x2) matrix.

Find principal stresses by finding the eigenvalues of the matrix

Matrixausfüllen

Cofactors Determinant and inverse of a 3x3 matrix.

Cofactors Determinant and inverse of a 3x3 matrix.

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

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

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

Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

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. 

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.