Show that a set of vectors {v1,v2,...,v5} in r^2 is linearly dependent whendim span{v1,v2,...v5} = 4

Answers

Answer 1

If dim span{v1,v2,...,v5} = 4, it means that the span of the set of vectors {v1,v2,...,v5} can be expressed as a 4-dimensional subspace of r^2. This implies that there are only 4 linearly independent vectors in the set {v1,v2,...,v5}. Therefore, there must be at least one vector in the set that can be expressed as a linear combination of the other 4 vectors. In other words, the set of vectors {v1,v2,...,v5} is linearly dependent.

To prove this, we can assume that v5 can be expressed as a linear combination of v1, v2, v3, and v4. That is, v5 = c1v1 + c2v2 + c3v3 + c4v4 for some constants c1, c2, c3, and c4. If we substitute this expression into the equation for the span of {v1,v2,...,v5}, we get:

span{v1,v2,...,v5} = span{v1,v2,v3,v4,c1v1 + c2v2 + c3v3 + c4v4}

Since v5 can be expressed as a linear combination of the other vectors, we can remove it from the span without changing the dimension of the span. Therefore, we have:

span{v1,v2,...,v5} = span{v1,v2,v3,v4}

Since the dimension of the span is 4, we conclude that the set {v1,v2,...,v5} is linearly dependent.

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Related Questions

which of the following best describes jim smiley? a clever and competitive b suspicious and aggressive c bored and annoyed d gentle and tranquil

Answers

The best description of Jim Smiley would be "a clever and competitive" individual.

Jim Smiley, a character created by Mark Twain in his short story "The Celebrated Jumping Frog of Calaveras County," is depicted as a shrewd and competitive person. He is known for his cunning nature and his desire to win in various contests and competitions. Jim Smiley's cleverness and competitive spirit are central to the story's plot and characterization.

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What is 2.7 rounded to the nearest whole number

Answers

Answer:

3

Step-by-step explanation:

if the decimal is 5 or more then u round up to the next number

4 or below then it stays that number

Hey there!


Fun fact:

If it’s BIGGER than 5 (or equal to 5), you round UPWARD & if it’s SMALLER than 5, you go DOWNWARD.


2 is SMALLER than 5 & 7 is BIGGER than 5


Thus, your answer should be: [3]


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

a box contains cards numbered 1 - 10. two cards are randomly picked with replacement. what is the probability of picking the card numbered three at least once?

Answers

The probability of selecting the card with the number three at least once is 1/10.

Given that,

1 through 10 cards are contained in a box. Two cards are chosen at random and replaced

To find : The probability of selecting the card with the number three at least once?

Probability (3 at first)  * Probability (3 at second) + Probability (3 at first)  *Probability (others at second) + Probability (others at first) *Probability (3 at second) = 1/10 * 1/0 + 1/10 *9/10 + 9/10*1/10

= 19/100 = 0.19

Here there are 10 cards,

So, probability of picking three is 1/10 and probability of picking others is 9/10

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Change 0.16 to equivalent fraction. ANS ______________.

Answers

Given the decimal number 0.16

We need to change it to a fraction

so,

\(\text{0}.16=\frac{16}{100}=\frac{4\times4}{4\times25}=\frac{4}{25}\)

So, the answer will be the equivalent fraction = 4/25

Use the dropdowns to complete the following statement.
The measure of an _____ angle of a triangle is _____ the _____ of its two ____ angles.



First dropdown: corresponding, interior, exterior, alternate

Second dropdown: equal to, less than greater than

Third dropdown: sum, quotient, difference, product

Fourth dropdown: adjacent, supplementary, remote interior, exterior​

Answers

Answer: exterior, equal, sum, remote
Explanation is edge

YALL JHITTS GO ADD MY T IK T OK

ITS >. * twoplayaany*

im following back

Answers

Answer:

Okay bestie ‼️

Step-by-step explanation:

How many degrees are in 3/4 of a full tum?​

Answers

Answer:

270 degrees

Step-by-step explanation:

Description: This lesson will explain that of the 360 degree full rotation of a circle, 3/4 of a rotation is 270 degrees.

What is the relationship between 3 squared and the square root of 9

Answers

Answer:

Three squared is 9 because 3*3=9 so therefore it is also the square root of 9

So the relationship is that 3 squared is 9 and the square root of 9 is 3

The circumference of a circular garden is 119.32 feet. What is the radius of the garden? Use 3.14 for t and do not round your answer.

Answers

Answer:

r = 19 ft

Step-by-step explanation:

Circumference, C is given as 119.32 ft

Circumference of a circle is given by the formula, 2πr

This means that,

C = 2πr, we're told to assume that π = 3.14

So therefore,

119.32 = 2 * 3.14 * r

r = 119.32 / 6.28

r = 19 ft

Convert 13000 milligrams into pounds. Round your answer to the nearest hundredth

Answers

Answer:

0.03 is the correct answer

Step-by-step explanation:

0.02866009 = 0.03

Please solve i will give brainliest

Please solve i will give brainliest

Answers

Answer:

Each item costs $6.46 dollars rounded to the nearest cent.

Step-by-step explanation:

All I did was divide 3133 divided by 482 is 6.45850622407.

But since this number is too big, I rounded it to the nearest cent.

So, the answer should be 6.46

Hope this helps! :)

please help me with the maths question attached below!!!

please help me with the maths question attached below!!!

Answers

Answer:

A)  y= -x+2

B) ( 2, 1)

Answer:

D, C

Step-by-step explanation:

1) y= -x+2

2) (2,1)

Find the function f, if: f'(x)=2/(x^3) + 4e^x + 5, f(-1)=1, f(1)=-1 (Note: Consider the domain and write the answer in ascending order of the variable).

Answers

Answer:

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

Step-by-step explanation:

We can find the function f(x) by integrating f'(x) with respect to x:

â«f'(x) dx = â«(2/(x^3) + 4e^x + 5) dx

f(x) = -1/x^2 + 4e^x + 5x + C

To find the constant C, we can use the given initial conditions:

f(-1) = 1 = -1/(-1)^2 + 4e^(-1) - 5 + C

C = 1 + 1/1 - 4e^(-1)

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

Therefore, the function f(x) is:

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

triangle interior angles theorem
answer and explain briefly

triangle interior angles theorem answer and explain briefly

Answers

Answer:

x=62

Step-by-step explanation:

(x+1)+ x+55=180

-55               -55 (take away the 55)

(x+1)+ x= 125 (take out of parenthesis)

x+1+ x= 125

2x+ 1= 125  (add the two x's together)

-1         -1        (take away the one)

2x= 124  (divide by 2)

     2

x=62

Compute the mean and variance of the following probability distribution. (round your answers to 2 decimal places.) x p(x) 7 0.10 14 0.20 21 0.25 28 0.45 click here for the excel data file

Answers

The mean of the probability distribution is 21.35 and the variance of the probability distribution is 51.3275

Given the probability distribution with values of x and corresponding P(x). We need to find the values of \(x^2\), x P(x), \(x^2\) P(x) to calculate mean and variance.

x       P(x)          \(x^2\)      x P(x)      \(x^2\) P(x)

7       0.10         49       0.7         4.9

14     0.20        196      2.8         39.2

21     0.25         441     5.25       110.25

28     0.45        784     12.6       352.8

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

∑x P(x) = 21.35

∑\(x^2\) P(x) = 507.15

Mean = ∑x P(x) = 21.35

and variance = ∑\(x^2\) P(x) - \((\sum x\ P(x) )^2\) = 507.15 - 455.8225 = 51.3275

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Use Desmos to graph and find a solution to the system
below
SHOW PROOF THAT THE SOLUTION WORKS IN EACH EQUATION

\(y=-3x-2\\2y=-x+6\)

Answers

Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
(-2,4)
Equation Form:
x=-2, y=4

a textbook company ships its books in boxes that can hold 30 pounds. one particular order calls for a shipment of 800 books. if each book weighs 1.4 kilograms, how many boxes will be required to fulfill this order

Answers

83 boxes are required to carry 800 books.

According to the question:

One Box can hold weight = 30 pounds

We know that ,  1 pound= 0.45 kg

hence, 30 pounds = 30 x 0.45 = 13.5kg  

hence,  one box can carry 13.5 kg of weight.

Now,

Weight of 1 book = 1.4 kg

So, Total Weight of 800 books= 1.4 x 800 kg

And , No. of boxes required to carry 800 books = (1.4 x 800)/13.5 = 82.96

                                                                             or approximately 83 boxes

Hence, 83 boxes are required to carry 800 books.

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PLEAS HELP CUZ I HAVE NO CLUE

Express the following relationship as a rate. This time, the rate should be minutes per page.

Reading 30 pages in 10 minutes

minute per page
hour per page
3 minutes per page
30 minutes per page

Answers

Answer: 3 minutes per page

Answer:

i agree with 3 minutes per page.  

Step-by-step explanation:

What is the distance between -3,3 and 4,-3

Answers

Answer:

-1,0

Step-by-step explanation:

-3 + 4

3-3

find the area of a triangle two sides of which are 8cm and 11 cm and the perimeter is 32​

Answers

to find:

the area of the triangle.

solution:

area of triangle= 1/2 × h × b

= 1/2 × 8 × 11

= 44cm^2

Answer:

44

Step-by-step explanation:

8+11=1932-19=13

area of a triangle=½×base×height

13~hypotenuese½×8×11=44cm

hope that hepls

incase u have any question coment below

Rewrite the ratio 6: 27 as an equivalent ratio of the form 1: n.
Give any decimals in your answer to 1 d.p.

Answers

The equivalent ratio of form 1 : n is 1 : 4.5

Here the ratio given is 6 : 27 and we have to convert this ratio into the form of 1 : n.

6: 27

= 6/27

Divide the numerator and the denominator by 6, then we get

1 / (27/6)

= 1/ 4.5

Which is equivalent to the ratio 1 : n.

Therefore the equivalent ratio is 1 : 4.5.

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which point is the center of a circle

Answers

Answer:

isnt it called the focus thats what i think

Step-by-step explanation:

Sarah invests £400 at 3%
interest for 6 years
Circle the correct calculation to
work out how much she has now.

Answers

Answer: £900

Step-by-step explanation:

mr. eaton is ordering sandwiches for a school picnic. the best deal is the 6-foot-long sandwich, which is cut into 4-inch-long pieces. mr. eaton expects 90 people to attend the picnic. he thinks each person will eat 2 pieces. how many 6-foot-long sandwiches should he order?

Answers

He should order 10 sandwiches of 6 foot long so, as to make sure that everyone will eat 2 pieces.

What is Conversion ?

We need to convert between the units in order to ensure the accuracy and to prevent measurement misinterpretation. For example, we do not measure the pencil's length in kilometres. In this situation, one must convert from kilometres (km) to centimetres (cm) (cm). In most cases, multiplicative conversion factors are used to convert one unit to another of the same quantity. Let's see how to change the length and mass units.

1 Feet = 12 Inches

So, 6 Foot = 72 inches

The Length of sandwich- piece is 4 inch

So, when we convert 6 foot long sandwich into 4 inch,

Then we get number of piece is = 72/4 = 18

From 6 foot long sandwich we get 18 pieces of 4 inch long sub.

Now, Total people who will attend picnic is 40

and each people will eat 2 pieces.

It means total number of piece required = 2 (90) = 180

Mr. eaton required 180 pieces of sandwiches.

Number of sandwiches = 180 / 1.8 = 10

He should order 10 sandwiches of 6 foot long.

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Given the expression 2m - 7x + 6 + 3x - 4 what are the CONSTANTS?

Answers

4 and 6 are constants

Answer:

The constants are 6 and 4

Step-by-step explanation:

They don’t have variables next to them

A baseball is hit at an angle of with the horizontal and with an initial velocity of v0 = 115 feet per second. An outfielder catches the ball 300 feet from home plate (see figure). A batter hits a baseball to an outfielder. There is a dashed line, a dashed curve, a marked angle and a distance given. The dashed line is horizontal and is at the same height as the top of the players heads. The ball travels the dashed curve from the horizontal line at batter, up and to the left, changing direction down to the left, to the horizontal line at the outfielder. The angle the curve makes with the horizontal line at the batter is labeled. The players distance apart is given as r = 300 ft. Find when the range r of a projectile is given by r = 1 32 v02 sin(2). (Enter your answers as a comma-separated list. Round your answers to one decimal place. )

Answers

The angle θ calculated from the range r of the projectile  is 11.2 degrees.

To find the angle θ when the range r of a projectile is given by r = 1/32 v0^2 sin(2θ), we can use the following steps:

Start with the given equation r = 1/32 v0^2 sin(2θ). Isolate the sin(2θ) term by dividing both sides of the equation by 1/32 v0^2. This gives us sin(2θ) = 32r/v0^2. Take the inverse sine of both sides of the equation to find 2θ. This gives us 2θ = sin^-1(32r/v0^2). Divide both sides of the equation by 2 to find θ. This gives us θ = sin^-1(32r/v0^2)/2. Now we can plug in the given values of r and v0 to find the angle θ.

r = 300 ft
v0 = 115 ft/s
θ = sin^-1(32(300)/(115)^2)/2
θ = sin^-1(32(300)/(13225))/2
θ = sin^-1(0.729)/2
θ = 22.4/2
θ = 11.2 degrees

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State the slope (m) and the y-intercept (b) for the problem below.
m
4. y=-2x + 4
b =

State the slope (m) and the y-intercept (b) for the problem below.m4. y=-2x + 4b =

Answers

Answer:

The slope is -2. The y intercept is 4.

Step-by-step explanation:

when sampling from a population with , which of the following sample means is more surprising? why? sample a: a random sample of 9 pell grant recipients with a mean award amount of $2750. sample b: a random sample of 36 pell grant recipients with a mean award amount of $2750.

Answers

Sample mean in sample b to be less variable and more representative of  population mean than sample mean in sample a.

Standard error measures the variability of sample means around the population mean.

It decreases as sample size increases.

Using the formula for the standard error of the mean,

Calculate the standard errors for each sample,

Standard error of sample a

= s/√(n)

= 850/√(9)

= 283.33

Standard error of sample b

= s/√(n)

= 850/√(36)

= 141.67

Where s is the sample standard deviation

And n is the sample size.

The standard error of sample b is smaller than the standard error of sample a.

Sample mean in sample b is more likely to be closer to true population mean than sample mean in sample a.

Therefore, sample mean b is more surprising as larger sample size makes it more likely and accurately represents population mean.

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Question 2 of 30
Which among the following is the correct range of value for the included angle of a V-belt?
O 10° to 200°
O 30° to 40°
O 70° to 80°
O 100° to 1200°

Answers

The correct range of value for the included angle of a V-belt is 30° to 40°. The V-belt provides power to the drive pulley. In the mechanical power transmission, V-belts are used in a large number of industrial and farm applications.

The V-belt is used for a smooth transition of power, and it is made from rubber and polymer materials with cords in the inside. It is commonly used in industrial machines, and it is easy to install and maintain. It is also used in power transmission with a high level of flexibility.

The correct range of value for the included angle of a V-belt is 30° to 40°.This angle is produced by joining the planes of the faces of the belt in the V section. It is the angle between the V-belt sides. The recommended value for the included angle of the V-belt is 36.5 degrees.

When the value is within this range, the V-belt functions optimally. A low included angle would result in a loose belt, whereas a high angle would result in a tight belt. In power transmission, V-belts are commonly used in a wide range of industrial and farm applications. The V-belt is used to provide power to the drive pulley. It is an essential mechanical component that ensures a smooth transition of power.

It is made of rubber and polymer materials, which make it durable and flexible. The V-belt's flexibility allows it to transmit power between pulleys located at different angles.The included angle is the angle between the sides of the V-belt. This angle is produced by joining the planes of the faces of the belt in the V section. The range of value for the included angle of a V-belt is 30° to 40°. The recommended value for the included angle of the V-belt is 36.5 degrees. When the included angle value is within this range, the V-belt functions optimally.

A low included angle would result in a loose belt, whereas a high angle would result in a tight belt.The V-belt's flexibility allows it to transmit power between pulleys located at different angles. The V-belt's grip on the pulley is an essential factor that affects the transmission of power. A low included angle would reduce the grip of the belt, resulting in slippage and reduced power transmission. In contrast, a high included angle would increase the grip of the belt, resulting in a higher level of power transmission.

The correct value of the included angle is critical to the V-belt's performance and longevity.

The correct range of value for the included angle of a V-belt is 30° to 40°. The recommended value for the included angle of the V-belt is 36.5 degrees. When the included angle value is within this range, the V-belt functions optimally. A low included angle would result in a loose belt, whereas a high angle would result in a tight belt. The V-belt's flexibility allows it to transmit power between pulleys located at different angles. The V-belt's grip on the pulley is an essential factor that affects the transmission of power.

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Find Joe's initial principal if he had $2,145 in
interest over 4 years at an interest rate of 5.5%

Answers

His final balance is $2,671.49.
And the total interest is $526.49

Answer:

see the screenshot below

Step-by-step explanation:

Find Joe's initial principal if he had $2,145 ininterest over 4 years at an interest rate of 5.5%
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