\(\displaystyle v=c_{1}v_{1}+c_{2}v_{2}\)
\(\displaystyle v_{1}=(-5,-2), \;\ v_{2}=(-1,-5)\)
\(\displaystyle -4(-5,-2)+4(-1,-5)=\fbox{(16,-12)}\)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Other way around:
We find scalars \(\displaystyle c_{1},c_{2}\) such that:
\(\displaystyle (16,-12)=c_{1}(-5,-2)+c_{2}(-1,-5)\)
equate components:
\(\displaystyle -5c_{1}-c_{2}=16\)
\(\displaystyle -2c_{1}-5c_{2}=-12\)
\(\displaystyle c_{1}=-4, \;\ c_{2}=4\)
Back where we started.
