Matrix multiplication. Has automatically generated "unresolved" matrix product to write in the solution.

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.

Use matrix multiplication to get an equation for \(k\) which is then to be solved.

To understand matrix multiplication in terms of linear combinations of column vectors.

Asking the student to create examples of two matrices which multiply to zero but are not themselves the zero matrix. Then getting the student to think about some features of these examples.

Easy intro questions to be done when the students have seen the "vector space axioms" but not as axioms, just in the context of \(\mathbb{R}^n\).

Calculating with vectors in \(\mathbb{R}^4\), including resolving brackets. The fixed vector size is so that a test is fair to all students.

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Simple questions on interval notation. If you are not randomising the order of your questions please turn on randomise choices in these questions.

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An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

Question 3 from module 1 mid module assessment task

A demo of the gap-fill part and its options.

Find the determinant of a $3 \times 3$ matrix.

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