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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Thomas Lynn
Answered 2022-01-08 Author has 1097 answers
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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Paul Mitchell
Answered 2022-01-09 Author has 240 answers
6. True. Vector space V is formed by an elements objects which are called as vectors.
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