The statement is either true in all cases or false. If false, construct a specific example to show that the statement is not always true. If v_1, ......, v_4 are in R^4 and v_3 = 2v_1 + v_2, then {v_1, v_2, v_3, v_4} is linearly dependent. Choose the correct choice below and, if necessary, fill in the answer boxes to complete your choice. a. True Because v_3 = 2v_1 +v_2, v_4 must be the zero vector. Thus, the set of vectors is linearly dependent. b. True. The vector v_3 is a linear combination of v_1 and v_2, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent. c. True. If c_1 =2, c_2 = 1, c_3 = 1, and c_4 = 0, then c_1v_1 + middot middot middot + c_4v_4 =0. The set of vectors is linearly dependent. d. False. If v_1 =, v_2 =, v_3 =, and v_4 = [1 2 1 2], then v_3 = 2v_1 + v_2 and {v_1, v_2, v_3, v_4} is linearly independent.

Answers

Answer 1

Answer: The correct option is (B).

True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.  

Step-by-step explanation:  

Given that;

If V₁ ....... V₄ are in R⁴ and V₃ = 2V₁ + V₂ then {V₁, V₂, V₃, V₄} is linearly dependent.  

Lets {V₁, V₂, V₃, V₄}  are linearly dependent

Then there exist a scalars C₁, C₂, C₃, C₄

So that C₁V₁ + C₂V₂ + C₃V₃ + C₄V₄ = 0

where at least one of the Ci ≠ 0.  

Take C₃ ≠  0 then we have V₃ = (C₁V₁ + C₂V₂ + C₄V₄) / C₃

V₃ is a linear combination of V₁, V₂ and V₄}

that is

Given V₃ = 2V₁ + V₂

⇒ 2V₁ + V₂ - V₃ = 0

⇒ 2V₁ + V₂ + V₃ + 0V₃ = 0

Here, C₁ = 1, C₂ = 1,  C₃ = -1 and C₄ = 0

So that {V₁, V₂, V₃, V₄} is linearly dependent.

therefore option B id the right answer.

- True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.  

Answer 2

B is the correct option. True, The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and the set is linearly dependent.  

If V₁ ....... V₄ are in R⁴ and V₃ = 2V₁ + V₂ then {V₁, V₂, V₃, V₄} is linearly dependent.  

What is meant by linearly dependent?

A set of vectors is linearly dependent if some vector can be expressed as a linear combination of the others.

Let's consider {V₁, V₂, V₃, V₄}  are linearly dependent

then there exist a scalars C₁, C₂, C₃, C₄

therefore, C₁V₁ + C₂V₂ + C₃V₃ + C₄V₄ = 0

where at least one of the Ci ≠ 0.  

Lets C₃ ≠  0 then we will get

V₃ = (C₁V₁ + C₂V₂ + C₄V₄) / C₃

V₃ is a linear combination of V₁, V₂, and V₄

which means V₃ = 2V₁ + V₂

2V₁ + V₂ - V₃ = 0

2V₁ + V₂ + V₃ + 0V₃ = 0

Here, C₁ = 1, C₂ = 1,  C₃ = -1 and C₄ = 0

therefore, {V₁, V₂, V₃, V₄} is linearly dependent.

So, option B is correct here.

True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others, and the set is linearly dependent.  

Learn more about linearly dependent here;

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Related Questions

30 g of pineapple are added to drink the drink rises 5 ml what is the density of the pineapple

Answers

Answer:

6g/mL

Step-by-step explanation:

Given parameters:

Mass of pineapple = 30g

Volume of rise  = 5mL

Unknown:

Density of pineapple = ?

Solution:

Density of a substance is the mass per unit volume. Mathematically, it is expressed as;

           Density  = [tex]\frac{mass}{volume}[/tex]

The volume is the rise in the pineapple drink.

 Insert the parameters and solve;

        Density  = [tex]\frac{30}{5}[/tex]

    Density  = 6g/mL

Write the equation of the line that passes through the points (1, 7) and (5, 15) using function notation.

Answers

Answer:

use the formula for a line through two points

[tex]y - y_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \times (x - x_{1})[/tex]

plug in the given points:

[tex]y - 7 = \frac{15 - 7}{5 - 1} \times (x - 1)[/tex]

[tex]y = \frac{8}{4} \times (x - 1) + 7[/tex]

[tex]y = 2 \times (x - 1) + 7 \\ y = 2x - 2 + 7 \\ y = 2x + 5[/tex]

6570 ÷ 16


410


410 1/16


410 3/8


410 5/8

Answers

Answer:

Exact Form:

3285

8

Decimal Form:

410.625

Mixed Number Form:

410

5

8

thats what i got i hope this helps

Step-by-step explanation:

It’s 410⅝. I used photomath :)

Which graph represents the linear equation y = 1?

Answers

Answer:

but there's no choices

Answer:

Since theres no options. The answer should look like this below:

<-------------------------------------------------------------------------------------------> x axis

Step-by-step explanation:

What is the following figure?
8 m
5 m
5 m
8 m
rhombus
rectangle
trapezoid
parallelogram

Answers

Answer:

rhombus

Step-by-step explanation:

you can't see what shape that is but Im doing this assignment right now I know what it looks like

Write the values of the 9s in 990.250. How are the values related?

Answers

Answer:

Leftmost 9: 900

9 between 9 and 0: 90

9 on left is worth 10 times 9 on right.

Step-by-step explanation:

990.250

The 9 at the left is in the hundreds place, so it represents 9 hundreds, so its value is 900.

The 9 between the 9 and the 0 is in the tens place, so it represents 9 tens, and its value is 90.

Since the places are right next to each other, the 9 on the left is worth 10 times the 9 on the right. Sure enough, 900 is 10 times 90.

How many millimeters are in 90 ounces?

Answers

Answer:2661615

Step-by-step explanation:

29573.5 is how many millimeters are in an ounce multiply that by 90 and you get 2661615

hope this helps

Answer:

you used two different types of things ounces measure mass and millimeters measure length

but I used google and it said 2.662e+6

the owner of an apple orchard ships apples in boxes that weigh 2 kilograms ( kg ) when empty. the average apple weighs 0.25 kg and the total weight of a box filled with apples is 12 kg. how many apples are packed in each box?

a. 14
b. 30
c. 40
d. 56

Answers

Answer: C=40

Step-by-step explanation: X=40 APPLES PER BOX.  

PROOF:

2+.25*40=12

2+10=12

12=12

A large ladder leans against a house with the base of the ladder 5.8 horizontal feet from
the base of the house. If the ladder has a slope of 3.3 feet per foot, at what height does the top of the ladder meet the house? (Round your answer to two decimal places.)
=_______ft

Answers

Answer:

At 19.14 feet the top of the ladder meet the house.

Step-by-step explanation:

It is given that,

A large ladder leans against a house with the base of the ladder 5.8 horizontal feet from  the base of the house.

Slope of the ladder, m = 3.3 feet/foot

We need to find at what height does the top of the ladder meet the house. Let it is h.

Base, b = 5.8 feet

It will form a right angle triangle

Slope=h/base

h = slope × base

h = 3.3 × 5.8

h = 19.14 feet

So, at 19.14 feet the top of the ladder meet the house.

The record low temperature in Pittsburgh, PA is ​-22°F. The record high is 103°F. What is the difference in the record high and the record low temperatures?

Answers

Answer:

The difference in the record high and the record low temperatures is 125°F

Step-by-step explanation:

Given a quantity T that varies in time, say T1 and T2, being T1 the initial value and T2 the final value.

The change or difference between the final and the initial values is:

T=T2-T1

The record low temperature in Pittsburgh, PA is T1=-22°F while its record high is T2=103°F

The difference is:

T=103°F - (-22°F)

Note both negative signs multiply to produce a positive sign, and a sum instead of a subtraction:

T=103°F + 22°F = 125°F

The difference in the record high and the record low temperatures is 125°F

find the quotient 4/7 divided by 1/5

Answers

Answer:

2 6/7

Step-by-step explanation:

You have to use the KEEP CHANGE CHANGE method. When you do this you end up with 4/7*5/1 which equals 20/7 and you then change that into a mixed number and you have your answer!

HOPE THIS HELPS!

Answer:

The answer is 2 6/7

Step-by-step explanation:

First, you set up the problem.

[tex]\frac{4}{7} / \frac{1}{5}[/tex]

Next, you change the division sign into multiplication

[tex]\frac{4}{7} x \frac{1}{5}[/tex]

Then you flip the 1/5

[tex]\frac{4}{7} x \frac{5}{1} \\[/tex]

Afterward, you multiply fractions straight across.

[tex]\frac{4}{7} x \frac{5}{1} =\frac{20}{7}[/tex]

Finally, you will simplify your answer into a mixed number.

[tex]\frac{20}{7} = 2 6/7[/tex]

Hope this helps!!

what is the product of 4/9 and 1/11? 4/99 5/99 9/44 1/4​

Answers

Answer:

4/99

Step-by-step explanation:

Multiply the numerator and den0ominater, then stack them

Answer:

4/99

Step-by-step explanation:

4/9 * 1/11

Multiply the numerators

4*1 = 4

Multiply the denominators

9*11 = 99

numerator over denominator

4/99

Mrs. Lewis received her paycheck this week in the amount of $535.75. She spent $76.98 on groceries, she paid her $59.95 phone bill and she spent $22.45 at the movies. How much did she have left over?

Answers

Answer:

376.37

Step-by-step explanation:

Answer:

376.37

Step-by-step explanation:

Mr.Milton had $1200 in his savings account at the beginning of the year. If his account has a balance of $1230 at the end of the year, what percent increase of his balance?

Answers

i’m guessing 30 not sure tho

Answer:

2.5%

Step-by-step explanation:

1230-1200 = 30

30÷1200 = 0.025

0.025 x 100 = 2.5

3 - +4 - = ?
4 4
OA.
3
7 -
4
OB.
4
3
8
OC.
8
OD. 7

Answers

The answer to this question is 8.


You just simplify it

WHICH ONE IS IT ?????!!!!!

Answers

Answer:

option 2 i think i hope i am right

Hey 675 m bike trails pass-through far is Meadow Aracely exhale the trail that cuts through Meadows flags meadow a measures 24 3/4m three legs measure 52.25 m on one leg measures 32 m the rest of the trail pass through forces how many meters of the trail pass through the forest

Answers

Answer:

436.75

Step-by-step explanation:

Answer:

436.75

Step-by-step explanation:

Which of the following is the solution to 17 - 2x = -11?

A. 3
B. -14
C. 14
D. -3

Answers

The answer is c because 2 times 14 is 28 and 17-28=-11

Answer:

14

Step-by-step explanation:

Divide each term by -2 and simplify

Hope this helped!

help me plz i promise i will mark brainliest​

Answers

Answer:

The answer is A.

Step-by-step explanation:

<2 and <3 are ____ angles

complementary

vertical

congruent

supplementary

Answers

Answer:

I think it's supplementary

Answer:

supplementary

Step-by-step explanation:

∠2 and ∠3 are supplementary angles

this means ∠2 and ∠3 are equal to 180

Let f(x)=(5)x+12. Evaluate f(0) without using a calculator.

Answers

Answer:

f(0) = 12

Step-by-step explanation:

You want to substitute 0 for x

f(0) = 5(0) + 12

f(0) = 12

Answer:

13

Step-by-step explanation:

Substitute 0 for x and simplify. f(0)=(5)0+12=1+12=13.

is the ratio of chocolate to ice cream comes in a book is 5:8 and the number of chocolate is 30 find the number of ice cream cones​

Answers

Answer:

48

Step-by-step explanation:

Answer:48

This is because I know that 5 times 6 is 30 so I would just have to do 8 times 6 which is 48

If you deposit $850 into an account which earns 6% yearly interest compounded monthly, how much will be in the account after 4 years, assuming you never withdraw money from the account? Round your answer to the nearest cent if necessary and do not include the dollar sign.

Answers

Answer:

1079.9

Step-by-step explanation:

A = P(1 + [tex]\frac{r}{n}[/tex])^nt

A: ending amount

P: principal (850)

r: interest rate in decimal form (.06)

n: compounding periods, 12 months in a year.

t: time in years (4)

   = 850(1 + .06/12)^12(4)

    = 850(1.005)⁴⁸

    = 850(1.2704891)

    = 1079.9157

Answer:

1079.92

Step-by-step explanation:

0.42 - 4) = 0.24 + 7)

Answers

Answer:

im sorry if not but i think its 7.24

Step-by-step explanation:

What is the domain of this function?​

Answers

Domain = inputs = x = { 1 , 2 , 3 }

Range = outputs = y = { 2 , -1 }

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

2 pay raises in 3 years unit rate

Answers

Answer:

1:1.5

Step-by-step explanation:

cut the 3 in half and cut the 2 in half

Look at this equation.
0.3x + 5. 14 = 2. 1x - 4.4
Which value of x makes the equation true?
0
-5.3
O - 4.1
O 4.1
O 5.3

Answers

Answer:

5.3

Step-by-step explanation:

1.8x = 9.4

x = 5.3

The value of x that makes the equation true is 5.3, the correct option is D.

What is an Equation?

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

The equations are useful in determination of unknown parameters.

The equation is,

0.3x + 5. 14 = 2.1x - 4.4

The equation is made of two expressions,

The expression 1 is : 0.3x + 5. 14

The expression 2 is : 2.1x - 4.4

The value of x that makes the equation true has to be determined.

0.3x + 5. 14 = 2.1x - 4.4

Grouping the like terms on one side.

5.14 +4.4 = 2.1x -0.3x

Solving the variables and constants

9.54 = 1.8 x

Dividing 1.8 on both sides of the equation.

x = 9.54 /1.8

x = 5.3

The value of x at which the equation is true is 5.3.

To know more about Equation

https://brainly.com/question/10413253

#SPJ6

Please help me I will give you the brainliest (I Didn’t spell that right but don’t care)

Answers

Answer:

positive

positive

negative

1 or -1

Step-by-step explanation:

Answer:

The product of two positive integers is always a positive

The product of two negative integers is always a positive

The product of a positive integer and a negative integer is always negative

The product of any integer and -1 is always a 1 or -1

Step-by-step explanation:

Hope this helps :)

How do I work this problem -16f+13=2f-11

Answers

Answer:

f = 4/3

Step-by-step explanation:

-16f + 13 = 2f - 11

24 = 18f

Divide

24/18 = f

4/3 = f

[tex] - 16f + 13 = 2f - 11[/tex]

Subtract sides -13

[tex] - 16f + 13 - 13 = 2f - 11 - 13 \\ [/tex]

[tex] - 16f = 2f - 24[/tex]

Subtract sides -2f

[tex] - 16f - 2f = 2f - 2f - 24[/tex]

[tex] - 18f = - 24[/tex]

Negatives simplifies

[tex]18f = 24[/tex]

Divided sides by 18

[tex] \frac{18}{18}f = \frac{24}{18} \\ [/tex]

[tex]f = \frac{4}{3} \\ [/tex]

_________________________________

And we're done.....♥️♥️♥️♥️♥️

The ages of three siblings are all consecutive integers. The sum of their ages is 39. How old is the youngest sibling?

could anyone explain this in a 2 part answer​

Answers

Answer:

Let x = the age of the youngest child

Let x + 1 = the age of the middle child

Let x + 2 = the age of the oldest child

x + x + 1 + x + 2 = 39

3x + 3 = 39

3x = 36

x = 12 years

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