## Calculus (3rd Edition)

${\bf{u}} = \frac{{11}}{{18}}{\bf{v}} + \frac{5}{{18}}{\bf{w}}$, where ${\bf{v}} = \left( {1,4} \right)$ and ${\bf{w}} = \left( {5,2} \right)$.
We express ${\bf{u}}$ as a linear combination of ${\bf{v}}$ and ${\bf{w}}$: ${\bf{u}} = r{\bf{v}} + s{\bf{w}}$ $\left( {2,3} \right) = r\left( {1,4} \right) + s\left( {5,2} \right)$ Now we solve the system of equations: $2 = r + 5s$ ${\ \ }$ and ${\ \ }$ $3=4r+2s$. So, we have $r=2-5s$. Substituting it in the equation $3=4r+2s$ gives $3=4(2-5s)+2s$. The solutions are $s = \frac{5}{{18}}$ and $r = \frac{{11}}{{18}}$. Thus, ${\bf{u}} = \frac{{11}}{{18}}{\bf{v}} + \frac{5}{{18}}{\bf{w}}$.