Question

Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use

s_{1}, s_{2}, and s_{3}, respectively,
for the vectors in the set.)

S = {(5, 2), (−1, 1), (2, 0)}

a) (0, 0) =

b) Express the vector *s*_{1} in the set as a
linear combination of the vectors *s*_{2} and
*s*_{3}.

s_{1} =

Answer #1

Write each vector as a linear combination of the vectors in
S. (Use s1 and s2, respectively, for
the vectors in the set. If not possible, enter IMPOSSIBLE.)
S = {(1, 2, −2), (2, −1, 1)}
(a) z = (−5, −5,
5)
z = ?
(b) v = (−2, −6,
6)
v = ?
(c) w = (−1, −17,
17)
w = ?
Show that the set is linearly dependent by finding a nontrivial
linear combination of vectors in the set whose sum...

Prove this:
Given that V is a linearly dependent set of vectors, show that
there exists a nontrivial linear combination of the vectors of V
that yields the zero vector.

Let
S={v1,...,Vn} be a linearly dependent set.
Use the definition of linear independent / dependent to show that
one vector in S can be expressed as a linear combination of other
vectors in S.
Please show all work.

1) Let S={v_1, ..., v_p} be a
linearly dependent set of vectors in R^n. Explain why it is the
case that if v_1=0, then
v_1 is a trivial combination of the other vectors
in S.
2) Let S={(0,1,2),(8,8,16),(1,1,2)} be a set of column vectors
in R^3. This set is linearly dependent. Label each vector in S with
one of v_1, v_2, v_3 and find constants, c_1, c_2,
c_3 such that c_1v_1+ c_2v_2+
c_3v_3=0. Further, identify the
value j and v_j...

Give an counter example or explain why those are false
a) every linearly independent subset of a vector space V is a basis
for V
b) If S is a finite set of vectors of a vector space V and v
⊄span{S}, then S U{v} is linearly independent
c) Given two sets of vectors S1 and S2, if span(S1) =Span(S2), then
S1=S2
d) Every linearly dependent set contains the zero vector

If v1 and v2 are linearly independent vectors in vector space V,
and u1, u2, and u3 are each a linear combination of them, prove
that {u1, u2, u3} is linearly dependent.
Do NOT use the theorem which states, " If S = { v 1 , v 2 , . . . ,
v n } is a basis for a vector space V, then every set
containing
more than n vectors in V is linearly dependent."
Prove without...

Prove that any set of vectors in R^n that contains the vector
zero is linearly dependent.

Problem 6.4 What does it mean to say that a set of vectors {v1,
v2, . . . , vn} is linearly dependent? Given the following vectors
show that {v1, v2, v3, v4} is linearly dependent. Is it possible to
express v4 as a linear combination of the other vectors? If so, do
this. If not, explain why not. What about the vector v3? Anthony,
Martin. Linear Algebra: Concepts and Methods (p. 206). Cambridge
University Press. Kindle Edition.

Determine whether the given set of vectors is linearly dependent
or independent. ?? = [5 1 2 1], ?? = [−1 1 2 − 1], ?? = [7 2 4
1]

1. Prove that if {⃗v1, ⃗v2, ⃗v3} is a linear dependent set of
vectors in V , and if ⃗v4 ∈ V , then {⃗v1, ⃗v2, ⃗v3, ⃗v4} is
also a linear dependent set of vectors in V .
2. Prove that if {⃗v1,⃗v2,...,⃗vr} is a linear dependent set of
vectors in V, and if⃗ vr + 1 ,⃗vr+2,...,⃗vn ∈V, then
{⃗v1,⃗v2,...,⃗vn} is also a linear dependent set of vectors in
V.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 20 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 4 hours ago

asked 5 hours ago