Question

If we want to express u=(22,57,-6) as a linear combination of
vectors *a = (4,9,3)* and *b=(-2,-7,6),* what are the
values of k and j?

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...

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 =

Using MATLAB solve:
The vectors v1=(1,-1,1), v2=(0,1,2), v3=(3,0,1) span R3. Express
w=(x,y,z) as linear combination of v1,v2,v3.

Give an example of a matrix equation representing a linear
combination of three vectors in R1, and two vectors in R3.

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 −...

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

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).

Let T be a linear transformation that is one-to-one, and u, v be
two vectors that are linearly independent. Is it true that the
image vectors T(u), T(v) are linearly independent? Explain why or
why not.

Exercise 6. Consider the following vectors in R3 . v1 = (1, −1,
0) v2 = (3, 2, −1) v3 = (3, 5, −2 ) (a) Verify
that the general vector u = (x, y, z) can be written as a linear
combination of v1, v2, and v3. (Hint : The coefficients will be
expressed as functions of the entries x, y and z of u.) Note : This
shows that Span{v1, v2, v3} = R3 . (b) Can R3 be...

1. Compute the angle between the vectors u = [2, -1, 1] and and
v = [1, -2 , -1]
2. Given that : 1. u=[1, -3] and v=[6, 2], are u and v
orthogonal?
3. if u=[1, -3] and v=[k2, k] are orthogonal vectors.
What is the
value(s) of k?
4. Find the distance between u=[root 3, 2, -2] and v=[0, 3,
-3]
5. Normalize the vector u=[root 2, -1, -3].
6. Given that: v1 = [1, - C/7]...

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