4) True. For vectors \(\displaystyle{v}_{{1}}\) and \(\displaystyle{v}_{{2}}\), the linear combination of \(\displaystyle{v}_{{1}}\) and \(\displaystyle{v}_{{2}}\) is \(\displaystyle{c}_{{1}}{v}_{{1}}+{c}_{{2}}{v}_{{2}}\) say u.

So u is linear combination if u can be written as sum of scalar multiplication.

5) False. Let \(\displaystyle{u}={2}{i}+{3}{j}\) and \(\displaystyle{v}={i}-{j}\) then \(\displaystyle{u}-{v}={\left({2}{i}+{3}{j}\right)}-{\left({i}-{j}\right)}={i}+{4}{j}\)

\(\displaystyle{v}-{u}={\left({i}-{j}\right)}-{\left({2}{i}+{3}{j}\right)}=-{i}-{4}{j}\)

\(\displaystyle\Rightarrow{u}-{v}\ne{v}-{u}\)

more over \(\displaystyle{u}-{v}=-{\left({v}-{u}\right)}\) is true.

So u is linear combination if u can be written as sum of scalar multiplication.

5) False. Let \(\displaystyle{u}={2}{i}+{3}{j}\) and \(\displaystyle{v}={i}-{j}\) then \(\displaystyle{u}-{v}={\left({2}{i}+{3}{j}\right)}-{\left({i}-{j}\right)}={i}+{4}{j}\)

\(\displaystyle{v}-{u}={\left({i}-{j}\right)}-{\left({2}{i}+{3}{j}\right)}=-{i}-{4}{j}\)

\(\displaystyle\Rightarrow{u}-{v}\ne{v}-{u}\)

more over \(\displaystyle{u}-{v}=-{\left({v}-{u}\right)}\) is true.