This question tests understanding of subscript notation for matrices

Adding and subtracting two 3x3 matrices.

Multiplication of $2 \times 2$ matrices.

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

Multiplication and adding matrices.

Multiplication of $2 \times 2$ matrices.

Determinant of n x m matrix by Laplace Expansion across top row.

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

Multiplication of $2 \times 2$ matrices.

Multiplication of  matrices of different sizes.

aij  notation and definition of the order of a matrix.

Exercises in multiplying matrices. 

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

Multiplication of $2 \times 2$ matrices.

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

Multiplication of  matrices of different sizes.

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".

No time limit - unlimited regeneration of questions allowed from these groups:

• Notation and Algebra
• Calculus - Differentiation
• Calculus - Integration
• Trigonometry and Matrices

Addition and subtraction of matrices; multiplication by scalar.

Multiplication of matrices.

Multiplication of matrices.

Multiplication of matrices.

Addition and subtraction of matrices; multiplication by scalar.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.

The interesting part about the implementation is the way the output is generated for "Advice".

Elementary Exercises in multiplying matrices. 

Based on Chapter 8, quite loosley.Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Cramers Rule applied to 3 simultaneous equations