(a) Show that w is a linear combination of u and v.
(b) Use your previous answer to show that u is a linear combination of v and w.
I did (a), but I'm not sure how I'm supposed to use it to to (b). What is the method here?
(a) Show that w is a linear combination of u and v.
(b) Use your previous answer to show that u is a linear combination of v and w.
I did (a), but I'm not sure how I'm supposed to use it to to (b). What is the method here?
it's established that $w$ is a linear combination of $u$ and $v$, i.e.
$w = \alpha u + \beta v,~\forall \alpha,~\beta \neq 0$
so
$u = \dfrac 1 \alpha \left(w - \beta v\right) = \dfrac 1 \alpha w - \dfrac \beta \alpha v$
and thus $u$ is a linear combination of $w$ and $v$