
Linear Independence
Quiz
•
Mathematics
•
University
•
Practice Problem
•
Hard
THIVYARATHI C
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
For what value(s) of ‘a’ are the following vectors linearly dependent:
(1, 5, −2), (0, 6, a) and (3, 13, −3)?
A.a = 3
B.a = -3
C.a = 9
D.a = -9
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Let {u, v, w, z} be independent vectors in a vector space V,then
A.{u + v, v + w, w + z, z + u} spans V.
B.{u + v, v + w, w + z, z + u} is independent.
C.Span {u + v,v + w, w + z,z + u} is contained in span {u, v, w z}.
D.{u + v, v + w, w + z, z + u} is a basis of V.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Let {v1, v2, … , vn} be dependent, nonzero vectors in a vector space V,then
A. There exists ij such that vi = kvj for some scalar k.
B. {v1} is dependent.
C. Span {v1, v2, …, vn} has dimension smaller than n.
D. {vi, vj} is independent for some i j
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Let {u, v, w} be an independent set in a vector space,then
A. u is a linear combination of v and w.
B. { u , v , u + v } is independent.
C. au + bv + cw = 0 for some nonzero scalars a, b and c.
D. { u , u + v , u + v + w } is independent.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Let V be a vector space, and let S be a subset of V . What does it mean when we say that W is closed under
scalar multiplication?
A. Whenever X is in V and c is a scalar, then cx is in W.
B. Whenever X is in W and c is a scalar, then cx is in V.
C. Whenever X is in W and c is a scalar, then cx is in W
D.Whenever X is in V and c is a scalar, then cx is in V.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Let V be a five-dimensional vector space, and let S be a subset of consisting of five vectors, Then S
A. Must be linearly independent, but cannot span V.
B. Can span V , but only if it is linearly independent, and vice versa.
C.Must be a basis of V.
Must be linearly dependent, and must span V.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Let V be a five-dimensional vector space, and let S be a subset of consisting of three vectors,Then S
A. Cannot span V , but can be linearly independent or dependent.
B. Must be linearly dependent, but may or may not span V .
C. Must be linearly independent, but cannot span V .
D. Must be linearly dependent, and must span V .
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