Multiplication and adding matrices.

Addition, subtraction and multiplication by a scalar for 2 x 2 matrices.

Multiplication of $2 \times 2$ matrices.

Addition, subtraction and multiplication by a scalar for 2 x 2 matrices.

Multiplication of $2 \times 2$ matrices.

A combination of tasks: checking which matrix products exist, calculating some of these products, calculating transpose matrices. Comparing product of transpose with transpose of product. Experiencing associativity of matrix multiplication. Not much randomisation, only in which matrix product is computed as second option.

Comprehensive solution written out in Advice.

Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

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

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

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

2x2 by ad-bc, 3x3 by Laplace expansion, properties of determinants

Multiplication of square and non square matrices, Identity matrices and zero matrices

(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 (2x2) matrix.

Multiple choice: select the correct (mxn) representation of the sizes of various matrices.

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Generates two sets of matrices that can be added and asks the student to add them. Will ensure that the dimensions in part a) are different to the dimensions in part b) to offer some variety.

Generates two sets of matrices that can be added and asks the student to add them. Will ensure that the dimensions in part a) are different to the dimensions in part b) to offer some variety.

No description given

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

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

Linear combinations of $2 \times 2$ matrices. Three examples.

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

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".

This exam test students understanding of determinants and inverses of 3x3 matrices.

This exam looks at the determinatns and inverses of 2x2 matrices