True , false Transcribed Image Text: 1. Let A be a 3×4 matrix. If nullity(A) = 3, rank(A) = 4.
2. Let A be an n x n matrix. If the columns of A are
linearly independent, then det(A) = 1.
3. If V is a 7-dimensional vector space and S is a set of 10
vectors, then the elements of S must be linearly
dependent.
4. In a vector space V, if the vectors a, b, and c span V,
then the dimension of V must be equal to 3.
5. The set of polynomials in x of degree at most 5 form a
vector space.
6. S = {v1, V2, … , Vn} is a linearly independent set if the
only solution to cv1 + C2v2 + *…*
+ CnVn = 0 has only
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the trivial solution.
7. Every vector space has a finite basis.
8. The dimension of Mm,n is m + n.
9. The additive inverse of a vector is unique.
10. A set W is a subspace of vector space V if W passes the
vector space axioms under any operations of addition
and scalar multiplication.