Question

Express the vector *v*⃗=[13, 35] as a linear combination
of *x*⃗=[−4, −5]and *y*⃗=[1, −5]

*v*⃗=v→= *x*⃗→+ *y*⃗→.

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...

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

5. Let V be a finite-dimension vector space and T : V → V be
linear. Show that V = im(T) + ker(T) if and only if im(T) ∩ ker(T)
= {0}.

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 =

1. Assume that V is a vector space and L is a linear function V
→ V.
a. Suppose there are two vectors v and w in V such that v, w,
and v+w are all eigenvectors of L. Show that v and w share the same
eigenvalue.
b. Suppose that every vector in V is an eigenvector of L. Prove
that there is a scalar α such that L = αI.

Let T be a 1-1 linear transformation from a vector space V to a
vector space W. If the vectors u,
v and w are linearly independent
in V, prove that T(u), T(v),
T(w) are linearly independent in W

1. Let ⃗u = −2[4,0,1]+[−1,3,−2] and ⃗v = 3[4,0,1]+5[−1,3,−2].
Let w⃗ = 3⃗u−⃗v. Express w⃗ as a linear combination of the vectors
[4, 0, 1] and [−1, 3, −2].
2. Let ⃗u and ⃗v be two vectors in Rn. Suppose that ||⃗u|| = 3,
||⃗u − ⃗v|| = 5, and that⃗u.⃗v = 1. What is ||⃗v||?.
3. Let ⃗u and ⃗v be two vectors in Rn. Suppose that ||⃗u|| = 5
and that ||⃗v|| = 2. Show that ||⃗u −...

write the vector w=(1,-4,13) as a linear combination of u1=(1,2,3),
u2=(2,1,1), u3=(1,-1,2)

Urgent!
Write down the definition of what it means for one vector to be
a linear combination of a collection of other vectors.
Can a given vector v be written as a linear combination of
vectors v1, v2, ...., vn in more than one way? Justify your
answer.
This is Linear Algebra

Find the vector in ℝ3 from point A=(x,y,z) to B=(−7,−2,−8)..
AB→=
The vector v⃗ in 2-space of length 7 pointing up at
an angle of π/6 measured from the positive x-axis.
v⃗=
(b) The vector w⃗ in 3-space of length 5 lying
in the yz-plane pointing upward at an angle of π/4 measured from
the positive y-axis.
v⃗ =
For what value(s) of tt does the equality
〈t3−6t,0.333333t2+4〉=〈0,6〉〈t3−6t,0.333333t2+4〉=〈0,6〉hold true?

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