2026-09-10T00:15:22.220330 image/svg+xml Matplotlib v3.10.9, https://matplotlib.org/ © EAGLE BEACON GLOBAL The diagram shows the vectors \(\mathbf{p}\) and ...
Question 1 Report
The diagram shows the vectors \(\mathbf{p}\) and \(\mathbf{q}\). Calculate the column vector \(\mathbf{p} + 3\mathbf{q}\), where \(\mathbf{p} = \begin{pmatrix} 2 \\ 7 \end{pmatrix}\) and \(\mathbf{q} = \begin{pmatrix} -1 \\ 3 \end{pmatrix}\). Show your working clearly.
Answer Details
First multiply every component of \(\mathbf q\) by 3:
\[3\mathbf q=3\begin{pmatrix}-1\\3\end{pmatrix}=\begin{pmatrix}-3\\9\end{pmatrix}.\]
Then add corresponding components:
\[\mathbf p+3\mathbf q=\begin{pmatrix}2\\7\end{pmatrix}+\begin{pmatrix}-3\\9\end{pmatrix}=\begin{pmatrix}2-3\\7+9\end{pmatrix}=\begin{pmatrix}-1\\16\end{pmatrix}.\]
The required column vector is \(\begin{pmatrix}-1\\16\end{pmatrix}\). [2 marks]
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