16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 5.3.10

Determinants

Mathematics — Linear Algebra · alternating-n-linear-functions-subspace

Problem

Let

F

be a field,

n

a positive integer, and

S

the set of

n \times n

matrices over

F

. Let

V

be the vector space of all functions from

S

into

F

. Let

W

be the set of alternating

n

-linear functions on

S

. Prove that

W

is a subspace of

V

. What is the dimension of

W