AS October 2020 Paper 1 Q4
4 The matrix \(\mathbf{M}\) is \(\begin{pmatrix} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{pmatrix}\).
(a)
(i) Calculate \(\det\mathbf{M}\). [1]
(ii) State two geometrical consequences of this value for the transformation associated with \(\mathbf{M}\). [2]
(b) Describe fully the transformation associated with \(\mathbf{M}\). [1]
| Scheme | Marks | AO |
|---|---|---|
| (i) \(\det\mathbf{M} = 1\) | B1 | 1.1 |
| [1] | ||
| (ii) It preserves volume | B1 | 1.1 |
| and orientation | B1 | 1.1 |
| [2] |
Notes
(a)(i)
B1: BC
| Scheme | Marks | AO |
|---|---|---|
| Rotation of \(90^\circ\) [anticlockwise] about O\(z\). | B1 | 1.1 |
| [1] |