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# Prove that the set of all n-linear functions over a field F is a vector space over F

ISBN: 9780130084514 53

## Solution for problem 18 Chapter 4.5

Linear Algebra | 4th Edition

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Linear Algebra | 4th Edition

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Problem 18

Prove that the set of all n-linear functions over a field F is a vector space over F under the operations of function addition and scalar multiplication as defined in Example 3 of Section 1.2 (p. 9).

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1.7 Linear Independence n - An indexed set of vectors {v ,…,1 } ip R is said to be linearly independent if the vector equation + + ⋯+ = 0 has only the trivial solution. ▯ ▯ ▯ ▯ ▯ ▯ The set {v 1…,v p is said be linearly dependent if their exist weights c 1…,c...

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Prove that the set of all n-linear functions over a field F is a vector space over F

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