A subspace is a subset of a vector space that satisfies the same properties as the vector space. This means that it is closed under vector addition and scalar multiplication.
R^3 (pronounced "R cubed") is a 3-dimensional vector space consisting of all ordered triples (x, y, z) where x, y, and z are real numbers.
To determine if a plane is a subspace of R^3, you can use the subspace test. This involves checking if the plane contains the zero vector, is closed under vector addition, and is closed under scalar multiplication.
No, a plane must be flat in order to be a subspace of R^3. A subspace must contain all possible linear combinations of its vectors, and a non-flat plane would not satisfy this property.
No, a plane must pass through the origin in order to be a subspace of R^3. This is because the zero vector is a necessary element of a subspace, and any plane that does not contain the origin would not contain the zero vector.