consider the vectors v1, v2,..., vm in rn. is span (v1,..., vm) necessarily a subspace of rn? justify your answer.

Answers

Answer 1

The span of a set of vectors is the set of all possible linear combinations of those vectors. So, if we have vectors v1, v2, …, vm in Rn, then the span of these vectors will be the set of all possible linear combinations of these vectors. This means that any vector in the span can be expressed as a linear combination of v1, v2, …, vm.

Now, to determine whether the span of these vectors is necessarily a subspace of Rn, we need to check the three subspace axioms: closure under addition, closure under scalar multiplication, and contains the zero vector.
Closure under addition: Let u and v be two vectors in span(v1, v2, …, vm). This means that u and v can be expressed as linear combinations of v1, v2, …, vm. Therefore, their sum u + v can also be expressed as a linear combination of v1, v2, …, vm, and so u + v is also in the span. Thus, the span is closed under addition.
Closure under scalar multiplication: Let c be any scalar and let u be any vector in span(v1, v2, …, vm). This means that u can be expressed as a linear combination of v1, v2, …, vm. Therefore, cu can also be expressed as a linear combination of v1, v2, …, vm, and so cu is also in the span. Thus, the span is closed under scalar multiplication.
Contains the zero vector: Since the zero vector can always be expressed as a linear combination of the vectors v1, v2, …, vm (by taking all coefficients to be zero), it follows that the span contains the zero vector.
Therefore, since the span of v1, v2, …, vm satisfies all three subspace axioms, it is necessarily a subspace of Rn.

To know more about Subspace Axioms visit:
https://brainly.com/question/30501720
#SPJ11


Related Questions

Could someone Please Help me with this?!?!?!?!

Answers

Answer:

-3

Step-by-step explanation:

To find slope use the equation [tex]y2 - y1 / x2 - x1[/tex]

1. Pick any two coordinate pairs to use in the equation. I'll choose (-2, 7) and (-1, 4).

2. Plug these coordinates into the formula. 4 - 7 / -1 - - 2

3.  Solve! -3/ 1 =  -3

4. The slope of this line is -3

What is 30% of 42?
I’ve given up on my hw pls help

Answers

Answer:

12.6 is the answer! happy to help ya :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

42(30/100)

12.6

Find x ( transversals relations )

Answers

Answer:

x = 12

Step-by-step explanation:

(8x - 34) and (5x + 2) are alternate angles and congruent, then

8x - 34 = 5x + 2 ( subtract 5x from both sides )

3x - 34 = 2 ( add 34 to both sides )

3x = 36 ( divide both sides by 3 )

x = 12

write a linear equation of a line that goes through (8,0) and (-6,7)

Answers

Answer:

Line equation: y=−0.5x+4

Slope: -0.5

Intercept: 4

Step-by-step explanation:

PLEASEEEEEE!!! help with this
PLEASE EXPLAIN HOW TO DO THIS LIKE IN STEPS AND EVERYTHING

Explain, in detail, the steps on how to factor the following trinomial.
3x^2+5x +2

Answers

Answer:

(3x+2)(x+1)

Step-by-step explanation:

Given the quadratic equaton;

3x^2+5x +2

Factorize

(3x^2+3x+)(2x+2)

Factor out the common value from each bracket

3x(x+1) + 2(x+1)

3x+2(x+1)

Hence the factored form is (3x+2)(x+1)

Find the number of terms in this polynomial. 7g7 + 10g4 – 6g3 + 3g2 - g​

Answers

Answer:

If you have more than 4 terms you say polynomial with the certain number of terms you have. So the answer to this is polynomial with 5 terms.

Hope this helps.

Write as an addition problem: 22 - (-8)

Answers

Step-by-step explanation:

22+8

I think this ans may help you

Are these two triangles congruent? *

Answers

Answer:

not congruent because none of the angles match

Answer:

Not Congruent

Step-by-step explanation:

No.

Two corresponding sides measure 8 and 4.

The other two corresponding sides measure 7 and 3.5.

In order to be congruent, each pair of corresponding sides has to be congruent.

Factor x⁴y² + x³y³.
A. x 3y 2(x + y)

B. x³y² (x + 1 )

C. x²y² (x + y)​

Answers

Answer:

A..........,..,......

Step-by-step explanation:

....,.............

help pleasseeeeeeeeee​

Answers

Answer:

B, C, E, F

Step-by-step explanation:

Challenge. A large university accepts ​60% of the students who apply. Of the students the university​ accepts, ​50% actually enroll. If 10,000 students​ apply, how many actually​ enroll?

Answers

10,000 x 0.6 = 6,000 are accepted
6,000 x 0.5 = 3,000 actually enroll

Answer: 3,000

Step-by-step explanation:

Apply= 10,000

University Accept= 10,000*60% = 6,000

Enroll= 6,000*50% = 3,000

I need a lot of heeelp pleaseee

Answers

Answer:

i think its mn

Step-by-step explanation:

its the 2 close to qs

Please help meeeee!!!!!!!!! What’s the answer????

Answers

Answer:

The answer would be y= |x-2| -1.

When graphing the answer B would be a larger quantity but A is the correct answer. Hope this helps :))

Please help
Write an equivalent expression for 3(3x + 5). Explain what property you used to write your equivalent expression.

Answers

Answer:  

distributive property  

9x+15  

Step-by-step explanation:  

The distributive property is whenever you have () and distribute until you have zero of these ()

The equivalent expression simply means write this equation differently.

Is the following triangle congruent by SAS, ASA, or SSS? Why?

Answers

Answer:

ASA

Step-by-step explanation:

As it is shown

m<A = m<Z

m<Y = m<C and

|YZ| = |AC| so the triangles are congruent by ASA

If you borrow $491 for one year at an interest rate of 9%, how much interest will you pay?

Answers

Answer:

44.19

Step-by-step explanation:

419*0.09=44.19

Suppose that $1,000 is deposited into an account that yields 0.85% interest, compounded annually.
How much money will be in that account at the end of 4 years? Round your answer to the nearest
cent

Answers

Answer:  1034.44 dollars

=====================================

Work Shown:

A = P*(1+r/n)^(n*t)

A = 1000*(1+0.0085/1)^(1*4)

A = 1034.43596172007

A = 1034.44

---------------------

Notes:

P = 1000 is the deposit or principalr = 0.0085 is the decimal form of the annual interest rate of 0.85%; we can say 0.85% = 0.85/100 = 0.0085n = 1 represents how many times per year we're compounding the money (ie annually)t = 4 = number of yearsThe result of 1034.44 dollars is only possible if you do not withdraw any of the money in the four year time period.

Mister Lincoln by juices and water for the school picnic a pack of their juices box cost $5 about the six water bottles cost $3 Mister Lincoln spends $94 for a Hyundai Sonata juice boxes and bottled water.

Answers

Answer:

10 packs of juice and 15 packs of water was bought by Mr. Lincoln

Step-by-step explanation:

Mr. Lincoln buys juice and water for the school picnic. A pack of 8 juice boxes costs $5. A pack of 6 water bottles costs $3. Mr. Lincoln spends $95 for 170 juice boxes and bottles of water.

Solution:

Let x represent the number of packs of juice boxes bought by Mr. Lincoln and let y represent the number of packs of water bottles bought by Mr. Lincoln.

Each pack of juice cost $5 while each pack of water cost $3. Mr. Lincoln spends $95, therefore:

5x + 3y = 95       (1)

Each pack of juice contain 8 juice boxes and each pack of water contain 6 water bottles. Since 170 juice boxes and bottles of water was bought, therefore:

8x + 6y = 170         (2)

Solving equations (1) and (2) simultaneously. Multiply equation (1) by 2 and then subtract equation (2) from the result to get:

2x = 20

x = 10

Substitute x = 10 in equation (1):

5(10) + 3y = 95

50 + 3y = 95

3y = 45

y = 15

Hence 10 packs of juice and 15 packs of water was bought by Mr. Lincoln

Quincy has box of cereal to eat over 6 days. If he splits the box into equal portions, how much will he eat each day?​

Answers

Answer:

1/6 of the cereal box

Step-by-step explanation:

Which Paris of triangle must be similar?

Answers

Triangles 1 and 2 are equilateral

The table shows two linear functions and the function values for different values of x.
Which expression represents h(x)?
A. (f ∙ g)(x)
B. (g + f)(x)
C. (f – g)(x)
D. (g – f)(x)

Answers

Answer:

the answer is A. (f ∙ g)(x)

Step-by-step explanation:

i got it wrong twice, and then it told me the answer

Answer:

its   A

Step-by-step sussy vent imposter baka :)  ;0

please help! thank u!​

Answers

Step-by-step explanation:

I cannot see the correct value so u check yourself. but this is the correct graph.

The price have changed from $120 to $75. By how many
percent did it change?
Plz show how you did it

Answers

Answer:

around 37%

Step-by-step explanation:

120 × (1 - 37%) = 120 × (1 - 0.37) = 75.6

if im being honest i used calculator . net's percentage calculator

Shirley went shopping in a mall. She reached the mall 12.5 minutes later than her usual time. While returning she took 20 minutes more than twice her usual time to reach home. If the usual time she takes to reach the mall is 40 minutes, find the total number of minutes Shirley spent going and coming back from the mall.

Answers

Answer:

Total time Shirley spent  going and coming back from the mall= 152.5 minutes

Step-by-step explanation:

Usual time it takes to reach mall from home = 40 minutes

New time she took to reach the mall=12.5 minutes later than her usual time

= 40 minutes + 12.5 minutes= 52.5 minutes

New time she took to reach home ( lets assume she followed the same route as coming from home in which she spends 40 minutes) =20 minutes more than twice her usual time to reach home.=20 minutes + 2(40)= 20 minutes  + 80 minutes

=100 minutes

Total time  going and coming back from the mall =52.5 minutes  +100 minutes = 152.5 minutes

What is the difference?

Answers

Answer:

I WAS WRONG PICK D

Step-by-step explanation:

I'm an idiot

Use multiplication to solve the proportion. a/6 = 15/2

Answers

Answer:

[tex]\frac{a}{6}[/tex] = [tex]\frac{15}{2}[/tex]

2a = 6 · 15

2a = 90

a = 45

Step-by-step explanation:

If the sumof two numbers is 4 and the sum of their squarea minus three times their product is 76, find the two numbers

Answers

Answer:

Step-by-step explanation:

If the sumof two numbers is 4 and the sum of their squarea minus three times their product is 76, find the two numbers

Let us represent:.

First number = x

Second number = y

If the sum of two numbers is 4

= x + y = 4

x = 4 - y

The sum of their squares minus three times their product is 76

x² + y² - 3xy = 76

We substitute 4- y for x

(4 - y)² + y² - 3(4 - y)y = 76

(4 - y)(4 - y) + y² - (12 - 3y)y = 76

16 - 4y - 4y - y² + y² - 12y - 3y² = 76

16 -20y - 3y² = 76

3y² + 20y - 16 + 76 = 0

3y² + 20y + 60 = 0

Three sisters have ages that are consecutive odd integers. The sum of their ages is 57. Find the age of each sister.

Answers

Answer:

The answer is 17 19 and 21

hope i could help!

what's the value of
[tex](2 \sqrt{2}) {}^{2} [/tex]
chess ?​

Answers

Answer:

jbtcxey5x6ivb

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

(2√2)^2

= (2^2× √2^2)

=(4×2)

=8

An escalator 152 feet in length rises to a platform and makes a 31° angle with the ground. Find the height of the
platform above the ground.

Answers

Answer:

78.3 or 78.29

Step-by-step explanation:

We are asked to find the height of the figure which is the vertical side of the triangle. We are given an angle and we are a side opposite of that angle( the height of the platform) and the hypotenuse 152. So we are going to use sine.

Opposite/Hypotenuse

We use this equation

[tex] \sin(theta) = \frac{opp}{hypo} [/tex]

Plug in the values

[tex] \sin(31) = \frac{x}{152} [/tex]

Which is about 78.29

Other Questions
The white owner of an apartment complex who refuses to rentto people of color is?Operating legallyNone of the abovePrejudicedDiscriminatingO A and B Which term describes a state with control over its internal affairs, independent of outside influence tennessee state fairgrounds sports arena I need Help answering these questions please (HELP!) now consider 0=-120. Draw the angle 0=-120 on the circle below. Make sure you rotate clockwise for the negative angle. It needs to be approximate, but not precise. How were roosevelts policies similar to and different from those of fascist leaders such as hitler and mussolini? nations should avoid war if possible. government must take care of its people. government should help manage the national economy. more powerful nations should rule less powerful ones. some nations are superior to others based on race. national policies should be enforced by armed squads. Caroline is concerned about her husband, Jeff. After being terminated from his job of over 15 years, Jeff was furious at first, but he has now withdrawn from Caroline and his family. He does not seem to experience any pleasure in any aspect of life. What can be inferred about this situation what is 7+6-8x5=???? what are the solutions to 5x^2 - x - 1 < 0 A roller-coaster car shown in the figure below is pulled up to point 1 where it is released from rest. Take y = 39 m .(Figure 1)Assuming no friction, calculate the speed at point 2.Express your answer to two significant figures and include the appropriate units.Calculate the speed at point 3.Express your answer to two significant figures and include the appropriate units.Calculate the speed at point 4.Express your answer to two significant figures and include the appropriate units. 1. On the basis of Home Depot's response to environmental issues, describe the attributes (power, legitimacy, urgency) of this stakeholder. Assess the company's strategy and performance with environmental and employee stakeholders. Which of the following skills or interventions is included at every level of prehospital emergency training? tenable.sc feed provides updates to the dashboard templates and which other objects The gas co2 is diffusin at steady state through a tube 20 cm long having a diameter of 1 cm and containing n2 at 350 k . the total pressur is constant at 101.3kpa . the partial pressure of co2 at one end is 456 mmhg and 76 mmhg at the end . the diffusivity is 0.167 cm2 /s at 298 k . calculate the mass rate of co2 if the partial pressure remains constant. Select the correct text in the passage.Which statement or phrase in the passage is a position held by opponents of corporate farming?State Question 777 was placed on the ballot by the Oklahoma legislature. It was designed to require courts to rule on any law that regulated farming and agriculture by employing "strict scrutiny." Had the measure passed, courts would have been required to overturn any challengedagriculture or livestock regulations that are not necessary for protecting a "compelling state interest." This new law would have made any existing law that restricted or regulated the farming industry in the state more vulnerable to lawsuits. In other words, State Question 777 wasdesigned to require the courts to apply the same standards to lawsuits that concerned agriculture and livestock as it did in cases that concerned free speech, gun ownership, and religious freedom. Some argue that State Question 777 would be used to prevent state and local governments from passing laws to protect small farmers and provide reasonable regulations. Amazon CloudWatch is designed to provide all of the following EXCEPT: 19Select the correct answer.Which exponential function has the greatest average rate of change over the interval [0, 2]?OA j(x) = 3(1.6)OB. An exponential function, f, with a y-intercept of 1.5 and a common ratio of 2.OC.OD.g(x)k(x) The phase of the business cycle when the economy is near or at full employment and the level of real output is at or near capacity is called a: When financial statements are revised to reflect the impact of a change in accounting principle, the ______ approach is used. Although the postworld war ii boom enriched millions of americans, it primarily affected the?