Coefficients by components

Coefficients by components

Secondary 4

It is given that \(\mathbf{u}=\begin{pmatrix}3\\ 1\end{pmatrix}\), \(\mathbf{v}=\begin{pmatrix}1\\ -2\end{pmatrix}\) and \(\overrightarrow{AB}=\begin{pmatrix}5\\ 4\end{pmatrix}\). Find the numbers \(m\) and \(n\) such that \(\overrightarrow{AB}=m\mathbf{u}+n\mathbf{v}.\)

Solution:

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Answer:\(m=2\), \(n=-1\)

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