Problems from Linear Combination of vectors

Development:

We want to find $\lambda$ and $\mu$ so that $\overrightarrow{w}=\lambda \overrightarrow{u}+\mu \overrightarrow{v}$. We have: $$(-5,2)=\lambda (-1,2)+\mu (1,2)=(-\lambda ,2\lambda )+(\mu ,2\mu )=(-\lambda +\mu ,2\lambda +2\mu )$$ De manera que: $$\begin{array}{r}-\lambda +\mu =-5\\ 2\lambda +2\mu =2\end{array}\}\Rightarrow \lambda =3,\mu =-2$$ We have just found values for $\lambda$ and $\mu$ for which $\overrightarrow{w}=\lambda \overrightarrow{u}+\mu \overrightarrow{v}$. Therefore, we can express $\overrightarrow{w}=(-5,2)$ as a linear combination of $\overrightarrow{u}=(-1,2)$ and $\overrightarrow{v}=(1,2)$.

Solution:

The vector $\overrightarrow{w}=(-5,2)$ can be espress as a linear combination of $\overrightarrow{u}=(-1,2)$ and $\overrightarrow{v}=(1,2)$: $\overrightarrow{w}=3\overrightarrow{u}-2\overrightarrow{v}$.

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