AS June 2018 Paper 1 Q1
1 The matrices \(\mathbf{A}\), \(\mathbf{B}\) and \(\mathbf{C}\) are defined as follows:
\[\mathbf{A} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}, \quad \mathbf{B} = \begin{pmatrix} 2 & 0 & 3 \\ 1 & -1 & 3 \end{pmatrix}, \quad \mathbf{C} = \begin{pmatrix} 1 & 3 \end{pmatrix}.\]Calculate all possible products formed from two of these three matrices. [4]
| Scheme | Marks | AO |
|---|---|---|
| \(\mathbf{BA} = \begin{pmatrix} 2 & 0 & 3 \\ 1 & -1 & 3 \end{pmatrix}\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix} = \begin{pmatrix} 11 \\ 8 \end{pmatrix}\) | M1 A1 | 1.1a 1.1 |
| \(\mathbf{AC} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}\begin{pmatrix} 1 & 3 \end{pmatrix} = \begin{pmatrix} 1 & 3 \\ 2 & 6 \\ 3 & 9 \end{pmatrix}\) | A1 | 1.1 |
| \(\mathbf{CB} = \begin{pmatrix} 1 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 & 3 \\ 1 & -1 & 3 \end{pmatrix} = \begin{pmatrix} 5 & -3 & 12 \end{pmatrix}\) | A1 | 1.1 |
| [4] |
Notes
M1: BA, AC or CB calculated with correct shape
allow one arith error for M1
A1: (3rd) deduct A1 for any incorrect products pursued