Question

Write each vector as a linear combination of the vectors in
*S*. (Use s_{1} and s_{2}, 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 is the zero
vector. (Use s_{1}, s_{2}, and s_{3},
respectively, for the vectors in the set.) S = {(1, 2, 3, 4), (1,
0, 1, 2), (1, 4, 5, 6)}

(0, 0, 0, 0) = ?

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

s_{3} = ?

Answer #1

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
s1, s2, and s3, respectively,
for the vectors in the set.)
S = {(5, 2), (−1, 1), (2, 0)}
a) (0, 0) =
b) Express the vector s1 in the set as a
linear combination of the vectors s2 and
s3.
s1 =

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.

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: If S = ~s1, . . . , ~sm is a system of vectors and B =
~v1, . . . , ~vn is a spanning system of a vector space V , then if
every ~vi ∈ B can be written as a linear combination of elements
from S, then S is also a spanning system of a vector space V .

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.

Determine if the vector v is a linear combination of the vectors
u1, u2, u3. If yes, indicate at least one possible value for the
weights. If not, explain why.
v =
2
4
2
, u1 =
1
1
0
, u2 =
0
1
-1
, u3 =
1
2
-1

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...

Hi. I have two questions about the linear algebra.
1. Prove that a linear transform always maps 0 to 0.
2. Suppose that S = {x, y, z} is a linearly dependent set. Prove
that every vector v in the span of the set S can be expressed as a
linear combination in more than one way.
Will thumb up for both answers. Thank you so much!

4. Prove the Following:
a. Prove that if V is a vector space with subspace W ⊂ V, and if
U ⊂ W is a subspace of the vector space W, then U is also a
subspace of V
b. Given span of a finite collection of vectors {v1, . . . , vn}
⊂ V as follows:
Span(v1, . . . , vn) := {a1v1 + · · · + anvn : ai are scalars in
the scalar field}...

Determine if the first vector is a linear combination of the
other two vectors. Show algebraically how you found your
answer.
2x^2 + 2x + 1, -x^2 + 2x + 1, -2x^2 + 2x + 1 in P2 (P subscript
2) (R).

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 15 minutes ago

asked 57 minutes ago

asked 1 hour 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 2 hours ago

asked 2 hours ago