Determine whether the set of vectors a1, 0, a3 under addition and scalar multiplication
Chapter 7, Problem 49(choose chapter or problem)
Determine whether the set of vectors \(\left\langle a_{1}, 0, a_{3}\right\rangle\) under addition and scalar multiplication defined by
\(\left\langle a_{1}, 0, a_{3}\right\rangle+\left\langle b_{1}, 0, b_{3}\right\rangle=\left\langle a_{1}+b_{1}, 0, a_{3}+b_{3}\right\rangle\)
\(k\left\langle a_{1}, 0, a_{3}\right\rangle=\left\langle k a_{1}, 0, a_{3}\right\rangle\)
is a vector space.
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