 True or False: 4. A vector is a linear combination if Tara Alvarado 2022-01-07 Answered
True or False:
4. A vector is a linear combination if u can be written as a sum of scalar multiples of those vectors
5. If $$\displaystyle{u},{v}\in{V}$$, then $$\displaystyle{u}-{v}=-{u}$$.
6. The objects in a vector space are called vectors.

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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.
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6. True. Vector space V is formed by an elements objects which are called as vectors.