Checking whether a given set is a plane or not. Depends on whether two vectors are parallel or not. Then checking whether the plane goes through the origin. This is not always obvious from the presentation.

Not randomised because it's the same as in our workbook.

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.

Abstract linear combinations. "Surreptitious" preview of bases and spanning sets, but not explicitely mentioned. There is no randomisation because it is just an abstract question. For counter-examples, any valid counter-example is accepted.

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.

Checking whether a given set is a plane or not. Depends on whether two vectors are parallel or not. Then checking whether the plane goes through the origin. This is not always obvious from the presentation.

Not randomised because it's the same as in our workbook.

easy vector addition and scalar multiplication, for practice after Section 1 of lectures.

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

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

The letters i, j and k are used to represent the standard 3D unit vectors.

This shows how to use variable name annotations inside \simplify to display a 3D vector in terms of the standard unit vectors $\boldsymbol{i}$, $\boldsymbol{j}$, $\boldsymbol{k}$

No description given

Assessment of NCDCS Unit 1 material.

Add three vectors by determining their scalar components and summing them.

Linear combinations of $2$ dimensional vectors. 

Review of NCDCS Unit 1 material.

This question uses the linear algebra extension to generate a system of linear equations which can be solved.

We want to produce an equation of the form $\mathrm{A}\mathbf{x} = \mathbf{y}$, where $\mathrm{A}$ and $\mathbf{y}$ are given, and $\mathbf{x}$ is to be found by the student.

First, we generate a linearly independent set of vectors to form $\mathrm{A}$, then freely pick the value of $\mathbf{x}$, and calculate the corresponding $\mathbf{y}$.

To generate $\mathrm{A}$, we generate more vectors we need, then pick a linearly independent subset of those using the subset_with_dimension function.

Resultant force

Resultant force

Resultant vector

Resultant force

Resultant force

Questions which ask the student to intepret vector diagrams in order to write out the components in terms of base vectors. Also addition and subtraction of vectors and vector magnitude.

This question introduces base vectors i and j and asks the student to interpret a JSXGraph diagram to write four vectors in terms of the base vectors. Further parts ask the student to add vectors and find a magnitude.

This question asks the student to interpret a JSXGraph diagram to write three vectors in terms of the base vectors. Each vector has both a horizontal and vertical component. Further parts ask the student to add vectors and find a magnitude. 

Find eigenvalues and eigenvectors of $A$ $2 \times 2$ matrix.