Julia Goedecke

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

Randomising the number of rows in the matrix, m, makes the marking algorithm for part c) slightly complicated: it checks whether it should include the third gap or not depending on the variable m. For the correct distribution of marks, it is then necessary to do "you only get the marks if all gaps are correct". Otherwise the student would only get 2/3 marks when m=2, so the third gap doesn't appear.

Determine for which value of \(t\) two vectors are parallel. In the first part, there is no real number \(t\) to make it work. In the second part, a value can be worked out.

Calculating with vectors of random size, including resolving brackets. Advice (i.e. solution) has conditional visibility to show only the correct size.

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.

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 student is asked to write a matrix with a certain property, or tick a box labelled "this is impossible" if it can't be done.

A custom marking algorithm on the gap-fill part first checks if the student ticked the box. If they did, their answer is marked correct if it really is impossible. If they didn't tick it, their matrix is checked against the required property.

Product of one of 2, 3, 5, 9, or 10 by a number up to 10. With hints to learn calculation rather than memorisation.

This is supposed to demonstrate allowing one of two different free variables in the student's answer, but only marked as correct if the same free variable is used in all gaps. The custom marking algorithm should extend to any number of gaps, and one could add more alternative answers to allow for more free variable names. It doesn't allow just any free variable name.