Question

Which sets are subspaces of R3?

Answer 1

In order to be a subspace of R3, a set must satisfy three conditions: closure under addition, closure under scalar multiplication, and contain the zero vector. Examples of subspaces in R3 include lines, planes, and the origin.

Step-by-step explanation:

In order for a set to be a subspace of R3, it must satisfy three conditions:

1. It is closed under addition.
2. It is closed under scalar multiplication.
3. It contains the zero vector.

Examples of sets that are subspaces of R3 include:

• The line passing through the origin and a point in R3.
• The x-y plane in R3.
• The origin itself.