1.
please explain.
Define/explain the following terms, and give a short example and non-example for each: Vector
space, subspace, additive closure, additive identity, additive inverse, commutative property,
associative property, distributive property, inherited properties, span of a set. True/False: Explain
why the statement is true, or give a specific counter-example: Multiplication of vectors is defined
for any vector space. We can divide by vectors in any vector space. We can subtract a vector in
any vector space. If + = , then = - . A vector space must have a but might not have a . Any linear
combination of two vectors from a subspace stays in that subspace.
Solution
1:multiplication of vector is defined for any vector space. ---true
If a multiplication is defined for the elements of a vector space, and if the vector space is closed
under this multiplication then it is called an algebra . For example, every field is an algebra.
2:false we can 't add or subtract two vectors unless they have the same number of components