Determine whether the statement is True or False. Justify your answer:A vector space is also a subspace of itself.
The statement is true
The statement is true. A vector space is indeed a subspace of itself.
To understand why, it is necessary to review the definitions of a vector space and a subspace.
A vector space is a set of objects called vectors, which satisfy certain properties. These properties include closure under vector addition and scalar multiplication, the existence of an additive identity element, the existence of additive inverses, and compatibility with the field of scalars (typically the real numbers or complex numbers).
On the other hand, a subspace is a subset of a vector space that also satisfies the properties of a vector space. In other words, a subspace is a vector space in its own right, but it is contained within a larger vector space.
Since a vector space satisfies all the properties of a vector space, it automatically satisfies the properties required for a subspace. Therefore, every vector space is a subspace of itself.
In conclusion, the statement “A vector space is also a subspace of itself” is true.
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