Moderate -0.5 This is a straightforward matrix multiplication exercise testing basic understanding of when products are defined (dimension compatibility) and routine calculation. It requires identifying valid products (AB, BA, AC, CA, BC, CB) based on dimensions and performing standard matrix arithmetic, but involves no problem-solving or conceptual depth beyond recall of the multiplication algorithm.
The matrices \(\mathbf{A}\), \(\mathbf{B}\) and \(\mathbf{C}\) are defined as follows:
$$\mathbf{A} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}, \quad \mathbf{B} = \begin{pmatrix} 2 & 0 & 3 \\ 1 & -1 & 3 \end{pmatrix}, \quad \mathbf{C} = (1 \quad 3).$$
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:
$$\mathbf{A} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}, \quad \mathbf{B} = \begin{pmatrix} 2 & 0 & 3 \\ 1 & -1 & 3 \end{pmatrix}, \quad \mathbf{C} = (1 \quad 3).$$
Calculate all possible products formed from two of these three matrices. [4]
\hfill \mbox{\textit{SPS SPS FM Pure 2025 Q1 [4]}}