1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
katrin2010 [14]
2 years ago
11

Given vectors u = (−1, 2, 3) and v = (3, 4, 2) in R 3 , consider the linear span: Span{u, v} := {αu + βv: α, β ∈ R}. Are the vec

tors (2, 6, 6) and (−9, −2, 5) in Span{u, v} ?
Mathematics
1 answer:
julia-pushkina [17]2 years ago
4 0

Answer:

(2,6,6) \not \in \text{Span}(u,v)

(-9,-2,5)\in \text{Span}(u,v)

Step-by-step explanation:

Let b=(b_1,b_2,b_3) \in \mathbb{R}^3. We have that b\in \text{Span}\{u,v\} if and only if we can find scalars \alpha,\beta \in \mathbb{R} such that \alpha u + \beta v = b. This can be translated to the following equations:

1. -\alpha + 3 \beta = b_1

2.2\alpha+4 \beta = b_2

3. 3 \alpha +2 \beta = b_3

Which is a system of 3 equations a 2 variables. We can take two of this equations, find the solutions for \alpha,\beta and check if the third equationd is fulfilled.

Case (2,6,6)

Using equations 1 and 2 we get

-\alpha + 3 \beta = 2

2\alpha+4 \beta = 6

whose unique solutions are \alpha =1 = \beta, but note that for this values, the third equation doesn't hold (3+2 = 5 \neq 6). So this vector is not in the generated space of u and v.

Case (-9,-2,5)

Using equations 1 and 2 we get

-\alpha + 3 \beta = -9

2\alpha+4 \beta = -2

whose unique solutions are \alpha=3, \beta=-2. Note that in this case, the third equation holds, since 3(3)+2(-2)=5. So this vector is in the generated space of u and v.

You might be interested in
Joel walked 2/5 of a mile to the store, 3/10 of a mile to the library, and 1/20 of a mile to the post office. Let x = the total
nadezda [96]
3/4 a mile is the answer
4 0
3 years ago
Tyler has two savings accounts that his grandparents opened for him. One of accounts pay 7 % annual interest, whereas the other
Dafna11 [192]

Answer:

$400 and $1,000

Step-by-step explanation:

Let us assume the x be the amount invested in 7% account

And, 600 + x be the amount invested in 9% account

Now the equation is

7x% + 9%(600 + x) = $118

0.07x + 54 + 0.09x = $118

0.16x = $118 -$54

0.16x = $64

x = $400

And, the other one is = $400 + $600 = $1,000

5 0
3 years ago
Randomly picking a blue card from a bag containing all blue cards
scoundrel [369]
What's the question
8 0
3 years ago
Read 2 more answers
Simplify 1/4(8x+16)+4x.
QveST [7]

Answer:

6x+4

Step-by-step explanation:

First thing to do is distribute 1/4 into the parenthesis. So 1/4 times 8x and 16. Which will give you 2x and 4. Then add like terms which will be 2x + 4x which is 6x. Then you have the 4 left over so your new equation is 6x+4.

6 0
3 years ago
Read 2 more answers
CAN SOMEONE SHOW ME HOW TO DO THIS PLEASE????????????????
morpeh [17]
For (h+g)(x) you just add the two functions:

(h+g)(x) = 4x + 2x^2

For (h•g)(x) you multiply them:

(h•g)(x) = 4x • 2x^2 = 8x^3

For (h-g)(x) you subtract them:

(h-g)(x) = 4x - 2x^2


For (h-g)(-2) you sub -2 into the equation we just created:

(h-g)(-2) = 4(-2) - 2(-2)^2
(h-g)(-2) = -8 - 2(4)
(h-g)(-2) = -8 - 8
(h-g)(-2) = -16
5 0
3 years ago
Other questions:
  • Can somebody explain area to me
    7·2 answers
  • How the bloody hell do I answer these? Please explain how you did it.
    10·1 answer
  • I need help ASAP please
    15·1 answer
  • HELP PLEASE!! The cost to fill a car's tank with gas and get a car wash is a linear function of the capacity of the tank. The co
    5·2 answers
  • The price of dress fabric is proportional to the length of fabric purchased. The graph shows this relationship.
    10·2 answers
  • An object travels 8 miles in 20 minutes at a constant speed. What is the
    12·1 answer
  • What inequalities are shown by this graph?​
    5·2 answers
  • The figure shows five points. A point has been translated right and up.
    12·2 answers
  • Can someone please help mee.
    15·1 answer
  • What is the quotient between 215÷9
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!