Question: In each of the following, a subset \(V\) of \(R^{3}\) is given.

1. \(V=\left\{\left(\begin{array}{c}x+y z \\ x+z \\ y\end{array}\right)\right.\) such that \(x_{i} y_{1} z\) arbitrary constant \(\}\)
   Is it closed under addition?
   Is it closed under scalar multiplication?
   Is it a vector subspace of \(R^{3}\) ?
2. \(V=\left\{\left(\begin{array}{c}x+y z \\ x+z \\ 1\end{array}\right)\right.\) such that \(x, y_{i} z\) arbitrary constant \(\}\) Is closed under addition Is closed under scalar multiplication Is a vector subspace of \(R^{3}\)
   Is it closed under addition?
   Is it closed under scalar multiplication?
   Is it a vector subspace of \(R^{3}\) ?
3. \(V=\left\{\left(\begin{array}{l}x \\ y \\ z\end{array}\right)\right.\) such that $x, y, z$ positive integer \(\}\)
   Is it closed under addition?
   Is it closed under scalar multiplication?
   Is it a vector subspace of \(R^{3}\) ?
4. \(V=\left\{\left(\begin{array}{l}x \\ y \\ z\end{array}\right)\right.\) such that \(\left.x y \leq 0\right\}\)

Is it closed under addition?

Is it closed under scalar multiplication?

Is it a vector subspace of \(R^{3}\) ?

Price: $2.99

Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document