Which of these is FALSE? a. Let V be an n-dimensional vector space. Then every s

Question

Which of these is FALSE?

a. Let V be an n-dimensional vector space. Then every set of n vectors linearly independent in V is a basis for V.
b. If S={v1,v2,,vm} is a set of linearly independent vectors in the vector space V, then every subset of S is also linearly independent.
c. Let A be an n×n matrix. If x0n is a nontrivial solution of Ax=0 , then x0 is an eigenvector of A.
d. Let V be an n-dimensional vector space. Then every n+1 vectors in V must be linearly dependent.
e. The set Pn of all real polynomials of degree n,n or less, is an n-dimensional vector space.

Explanation / Answer

I believe it is B because only one vector needs not be dependent for independence. so if had only one and it were removed then the matrix could become linearly dependent.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.