Suppose $a$ lies in the span of a set of independent vectors $E$. Now, if $a=b+c$, is it also the case that $b$ and $c$ lie in the span o the same set of vectors $E$?
if the question is obscure, please let me know. thanks in advance.
Suppose $a$ lies in the span of a set of independent vectors $E$. Now, if $a=b+c$, is it also the case that $b$ and $c$ lie in the span o the same set of vectors $E$?
if the question is obscure, please let me know. thanks in advance.
No. For example, try $b = e_1 - e_2$ and $c = e_1 + e_2$ where $e_1$ and $e_2$ are independent vectors. Then $a = 2 e_1$ is a linear combination of $e_1$, but $b$ and $c$ are not.