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# please explain- Define-explain the following terms- and give a short.docx

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# please explain- Define-explain the following terms- and give a short.docx

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

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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

.

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### please explain- Define-explain the following terms- and give a short.docx

1. 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