Vector Spaces and Subspaces, Addition and Scalar Multiplication

Please view the attached files to see the expressions which are in question for parts A and B.
1. A) Determine whether the following sets are vector spaces, in each case giving reasons for your answer.
B) Determine whether W is a subspace of the given vectorspace V.

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Solution Summary

In this solution, the concepts of vector spaces and sub spaces, addition and scalar multiplication are investigated. The solution is detailed and well presented in both a pdf. file and a Word document.

... iii) Nature of the intersection and union of sub spaces. Vector Space A non-empty set of vectors V is ... over a scalar field when the vector addition and scalar...

... Then. For and and. Thus, and . Hence is a subspace of . ... Notes:- Vector Spaces A non-empty is said to be a vector space over a field if (a) is an abelian group ...

... Notes:- Vector Spaces A non-empty is said to be a vector space over a field if (a) is an abelian group under ...Subspace Let be a vector space over the field . ...

... x]] is a vector space over F with the given addition and scalar... Question 3: Suppose that U and W are finitely-generated subspaces of a vector space V. Prove ...

... a0 + a1x + a2x^2 + a3x^3 for which a3 ≠ 0 is a subspace in the vector space R3[X] of ... 9)Determine whether w is in span of the given vectors v1, v2,.. ...

... a) choose [a,b]=[0,1]. Decide for each of the following subsets if it is a subspace. ... Let u and v be two vectors in a vector space v over {see attachment} . ...

... So U is a subspace if and only if for two vectors. ... U = {(a, b,1) : a, b ∈ } is not a subspace since: v ... such that for every vector v in the vector space V we ...

... P is a subspace means that P satisfies both properties: a subspace of a vector space is a subset that is closed under both addition and scalar multiplication. ...