Moderate -0.8 This is a straightforward matrix multiplication exercise testing basic understanding of when products are defined and how to compute them. Students need to check dimensions (3×1, 2×3, 1×2) and calculate AB, BA, AC, CA, BC, CB where defined. While it requires careful organization and arithmetic, it involves only routine application of matrix multiplication rules with no problem-solving or conceptual insight required.
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]
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]
\hfill \mbox{\textit{OCR MEI Further Pure Core AS 2018 Q1 [4]}}