T/F : Find a 3 by 3 matrix A which is not invertible, but where no two columns are scalar multiples of each other, and no two rows are scalar multiples of each other

Answers

Answer 1

False.

It is not possible to find a 3 by 3 matrix A which is not invertible, but where no two columns are scalar multiples of each other, and no two rows are scalar multiples of each other.



It is not possible to find a 3 by 3 matrix A which is not invertible, but where no two columns are scalar multiples of each other, and no two rows are scalar multiples of each other.

This is because if no two columns of A are scalar multiples of each other, then the columns are linearly independent, and the rank of A is at least 3. Similarly, if no two rows of A are scalar multiples of each other, then the rows are linearly independent, and the rank of A is also at least 3. Since A is a 3 by 3 matrix, it follows that the rank of A is at most 3. Therefore, the only way for A to have rank 3 is for A to be invertible.

So, any 3 by 3 matrix A that is not invertible must have either two columns that are scalar multiples of each other, or two rows that are scalar multiples of each other.

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Related Questions

There is a plan being discussed to build a skate park in a neighborhood. The city wants to have feedback to see if this is going to be used and well received by the community. The city sends out a newsletter and asks for people to respond with their opinion.
Biased or Unbiased?

Answers

The given representation of the sample is an unbiased sample.

What are biased and unbiased samples?

When some population members have a higher or lower sampling probability than others, the sample is biased.

This includes choosing or sampling people according to their hobbies, gender, or age.

Therefore, an unbiased sample must be representative of the entire population under investigation.

Given, There is a plan being discussed to build a skate park in a neighborhood.

The city sends out a newsletter and asks for people to respond with their opinion.

As they have sent newsletters and asked random people for feedback this would be an unbiased sample.

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an educational researcher is analyzing the test scores for statistics students taught using two different methods: a traditional method and a web-based self-paced method. randomly selected students from both groups were given the same test; the data is shown below: traditional web-based self-paced sample size: 80 40 mean test score: 84 81 population variance: 28 40 this data is then used (along with a .05 significance level) to test the claim that the mean test score for the web-based self-paced method is lower than that of the traditional method. what is the p-value for the test?

Answers

The p-value for the test is 0.01.

Test the assertion that the web-based self-paced technique's mean test score is lower than that of the conventional method.

u1 = u2

u1 > u2

Test statistics is

\(t=\frac{\bar{x}-\bar{y}}{\sqrt{\frac{\sigma 1^2}{n1}+\frac{\sigma 2^2}{n2}}}\)

\(t=\frac{84-81}{\sqrt{\frac{28}{80}+\frac{40}{40}}}=2.58\)

t=2.58

Compute the value of the test statistic as given

t = (84 - 81) / ((28/80) + (40/40)) = 2.58

Determine the degree of freedom.

df = ((28/80) + (40/40))² / ((28/80)² / (80-1) + (40/40)² / (40-1)) = 77.54

Next find the p-value using a t-test to calculate the p-value. This can be done using a statistical software package or online calculator.

p-value = 0.01

The p-value for this problem is 0.01, which means that there is a 1% chance that the results could have occurred by chance.

Hence , The p-value is less than 0.05, so we skip the null hypothesis.

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Can someone help me answer the second question please. I don't understand ​

Can someone help me answer the second question please. I don't understand
Can someone help me answer the second question please. I don't understand

Answers

The equation for the total number of coins is given as follows:

x + y = 12.

The equation for the total value of the coins is given as follows:

0.1x + 0.05y = 2.4.

How to define the system of equations?

The variables for the system of equations are defined as follows:

Variable x: number of 10 cent coins.Variable y: number of 5 cent coins.

They have a total of 12 coins, hence the equation for the total number of coins is given as follows:

x + y = 12.

Considering the value of each coin, 10 cents = 0.1 and 5 cents = 0.05, the  equation for the total value of the coins is given as follows:

0.1x + 0.05y = 2.4.

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The equation for the total number of coins is given as follows:

x + y = 12.

The equation for the total value of the coins is given as follows:

0.1x + 0.05y = 2.4.

How to define the system of equations?

The variables for the system of equations are defined as follows:

Variable x: number of 10 cent coins.Variable y: number of 5 cent coins.

They have a total of 12 coins, hence the equation for the total number of coins is given as follows:

x + y = 12.

Considering the value of each coin, 10 cents = 0.1 and 5 cents = 0.05, the  equation for the total value of the coins is given as follows:

0.1x + 0.05y = 2.4.

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can you answer my question plz?
whats the slope (-6,1) (4,-4)?

look people be lying bruh..........
(in the picture down below)

can you answer my question plz? whats the slope (-6,1) (4,-4)?look people be lying bruh..........(in

Answers

Answer:   The slope for this line is m=−12.

T.Step-by-step explanation:

To find the slope of a line passing through two points you use the formula: m=y2−y1x2−x1.

Brainllest plz!!

Hope i helped!!

I would like a little help please.

Gru has 20 minions. The minion population increases by 20 each week. El Macho has 80 evil minions. His population decreases by 10 minions each week. When will they have the same number of minions? How many minions??

x:

y:

solution:

system:


meaning of solution:

Answers

in 2 weeks and it will be 60 minions

4. A prism has an area of cross-section of 89 cm². The volume of the prism is
4895 cm?. Find the height of the prism.

Answers

Answer:

55 cm

Step-by-step explanation:

height = 4895/89 = 55 cm

I really need the answer now pls help me asap!!

I really need the answer now pls help me asap!!

Answers

Answer:

1 A

2 B

3 D

4 B

5 A

6 D

7 C

8 B

9 C

Step-by-step explanation:

1 A

2 B

3 D

4 B

5 A

6 D

7 C

8 B

9 C

Use the multiplication to expand the expression below. Then computer and/or simplify
(-3c)^4

Expanded form: ?
Answer: ?

Answers

The expanded expression is: (-3)⁴*c⁴

And the simplified expression is written as: 81*c⁴

How to expand and simplify the expression?

Here we have the expression:

(-3c)⁴

To expand this we need to remember that the exponents are distributive under products, then we can expand the expression to get the expansion:

(-3)⁴*c⁴

Now to simplificate it, we can simplify the first factor, the fourth power of the number -3 is:

(-3)⁴ = 81

Now replace that in the expression written above, then we will get the simplified expression:

81*c⁴

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Help me with this please, Factor it

Help me with this please, Factor it

Answers

Answer:

Hopefully this can help

Step-by-step explanation:

Help me with this please, Factor it

Answer:

\(3x^{2} (x+5)(x-5)\)

Step-by-step explanation:

Given that y = 9 cm and 0 = 23°, work out x rounded to 1 DP.
у
х
00
PLEASE HELP

Given that y = 9 cm and 0 = 23, work out x rounded to 1 DP.00PLEASE HELP

Answers

Answer:

x ≈ 3.5 cm

Step-by-step explanation:

Using the sine ratio in the right triangle

sin23° = \(\frac{opposite}{hypotenuse}\) = \(\frac{x}{y}\) = \(\frac{x}{9}\) ( multiply both sides by 9 )

9 × sin23° = x , then

x ≈ 3.5 cm ( to 1 dec. place )

Write a unit rate that compares the quantities describe 50 hockey players on 5 teams

Answers

Answer:

10

Step-by-step explanation:

50 divded by 5=10

5 divided by 5=1

10/1=10

HELP ME PLEASE, I need help and don’t understand at all !

HELP ME PLEASE, I need help and dont understand at all !

Answers

okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

Suppose that Amanda raises chickens whose eggs have a mean weight of 57 grams and a
standard deviation of 6 grams. Her friend Bernardo also raises chickens, and their eggs have a
mean weight of 54 grams and a standard deviation of 8 grams.
They decide to have a contest where they'll each randomly select 60 of their eggs, calculate the
mean weight, and look at the difference between their sample means (A - TB).
What are the mean and standard deviation (in grams) of the sampling distribution of TA - TB? by

Suppose that Amanda raises chickens whose eggs have a mean weight of 57 grams and astandard deviation

Answers

Therefore ,xa - xb = 3 and σa - σb = √(6/60) + (8/60) respectively are the units that were chosen and standard deviation difference.

The definition of standard deviation

How far the data points deviate from the mean is determined by descriptive statistics standard deviation. It quantifies how values are spread out over the sample data and gauges how far out of the mean data points are.

Here,

Given:

For Amanda's chicken, xa = 57 grammes is the average weight.

Chicken from Bernardo weighs, on average, 54 grammes.

The sample mean's difference is -

=> xa - xb

=> 57 - 54

=> 3

The chicken from Amanda's recipe had a standard deviation of 6 grammes.

The Bernardo's chicken standard deviation is b = 8 grammes.

N = 60 total observations were made.

The standard deviation formula is -

σ = √(x - μ)/n

σa - σb = √(6/60) + (8/60)

The figures are as follows: mean = 3; standard deviation = ((6/60) + (8/60).

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suppose it is certain that an earthquake will occur someday. what is the probability (to the nearest percent) that it will occur while you are at work? assume you are at work 8 hours per day, 250 days per year.

Answers

To the nearest percent, the probability that an earthquake will occur while you are at work is approximately 23%.

The probability that an earthquake will occur while you are at work can be calculated by dividing the number of hours you are at work by the total number of hours in a year.
Step 1: Calculate the total number of hours in a year:
There are 24 hours in a day, so multiplying 24 by 365 (the number of days in a year) gives us 8,760 hours in a year.
Step 2: Calculate the number of hours you are at work in a year:
Since you work 8 hours per day, multiply 8 by 250 (the number of days you work in a year) to get 2,000 hours.
Step 3: Calculate the probability:
Divide the number of hours you are at work (2,000) by the total number of hours in a year (8,760) and multiply by 100 to convert to a percentage.
Probability = (2,000 / 8,760) * 100 = 22.83%
Therefore, to the nearest percent, the probability that an earthquake will occur while you are at work is approximately 23%.

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There was a large crowd at a symposium. 6 times the number of people who attended the symposium was 3034 more than
1
7
of the attendance. How many people attended the symposium?

Answers

The total number of people who attended the symposium from a large crowd is equal to 518.

Let us consider the number of people who attended the symposium x.

6 times the number of people who attended the symposium is 3034 more than 1/7 of the attendance.

This can be written as,

6x = (1/7)x + 3034

To solve for x,

First simplify the equation by multiplying both sides by 7 to get rid of the fraction,

42x = x + 21238

Next, isolate x on one side of the equation by subtracting x from both sides,

⇒ 41x = 21238

Finally, solve for x by dividing both sides by 41,

⇒ x = 518

Therefore, number of people who attended the symposium is equal to 518.

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You are dealt one card from a standard 52-card deck. Find the probability of being dealt in a queen?

Answers

Answer:

1/13 or 7.69%

Step-by-step explanation:

A standard 52 card deck has 4 queens. So the probability of being dealt a queen is:

P(Queen) = 4/52

= 1/13

The probability is 1/13. To find the percent, divide 1÷13 and then times by 100.

1÷13 = 0.0769

0.0769× 100 = 7.69

This is 7.69%

Show that the function f defined by {1 (x,y) = (0,0)
f(x, y) = {x^2+y/x+y (x,y) ≠ (0,0)
is not continuous at (0,0).

Answers

Answer:It has been shown that the function is not continuous at (0,0).

The question is about finding the function's continuity at (0,0). Given a function f such that:

{1 (x,y) = (0,0)f(x, y)

= {x^2+y/x+y (x,y)

≠ (0,0)

It is required to show that the function is not continuous at (0,0).Solution:The function is given by:

{1 (x,y) = (0,0)f(x, y)

= {x^2+y/x+y (x,y)

≠ (0,0)

To prove the function is not continuous, we will have to show that limf(x,y) when (x,y) → (0,0) does not exist. Let us try to find limf(x,y) when (x,y) → (0,0).

Let y=0.

Hence,f(x,y) = f(x,0)

= {x^2/x}

= x

when x ≠ 0. Now when y = 0,x → 0, f(x,0) → 0.

This indicates that the limit of the function exists when x approaches 0.Now let x=0.

Hence,f(x,y) = f(0,y)

= {y/y} = 1 when y ≠ 0. Now when

x = 0,y → 0, f(0,y) → 1.

This indicates that the limit of the function exists when y approaches 0.

Now, we put x=y

= t.

Hence,f(t,t) = {2t/t+t}

= 1

when t ≠ 0. Now when t → 0,f(t,t) → 1.

This indicates that the limit of the function exists when x and y approach 0 simultaneously.Now, we have found the limit of the function along x and y axis and also when x=y. If limf(x,y) when (x,y) → (0,0) exists, it should be equal to all the limits that we have found so far.

Hence the limit should be equal to 0 and 1, which is a contradiction. This means that the limit does not exist when (x,y) → (0,0).

Therefore, the function is not continuous at (0,0).

Hence, it can be concluded that the given function is discontinuous at (0,0).

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the number of buses arriving at a bus stop in any interval of minutes is a poisson random variable on average, a bus arrives every minutes. (a) for an interval of minutes, (b) what is the probability of buses arriving in a -minute interval? (c) what is the probability of no buses arriving in a -minute interval? (d) how much wait time is necessary to guarantee at least one bus with % probability?

Answers

(a) The mean number of buses arriving in any interval of minutes is λ = 1.

(b) The probability of buses arriving in a t-minute interval is P(X > 0) = 1 - P(X = 0), where X is a Poisson random variable with parameter λt.

P(X = 0) = \(e^{(-λt)}\) = \(e^{(-t)}\)Therefore, P(X > 0) = 1 - \(e^{(-t)}\).

(c) The probability of no buses arriving in a t-minute interval is P(X = 0) = \(e^{(-λt)}\) = \(e^{(-t)}\).

(d) The probability of at least one bus arriving in a t-minute interval is

P(X ≥ 1) = 1 - P(X = 0) = 1 - \(e^{(-t)}\).

To guarantee at least one bus with a certain percentage of probability, we need to solve the inequality:

1 - \(e^{(-t)}\) ≥ p

where p is the desired probability. Solving for t, we get:

t ≥ -ln(1-p)

Therefore, the minimum wait time necessary to guarantee at least one bus with a probability of p is -ln(1-p) minutes.

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3. Which graph represents a proportional relationship? Explain. Graph A Graph B ty Graph C​

3. Which graph represents a proportional relationship? Explain. Graph A Graph B ty Graph C

Answers

Answer:

graph B because you can tell that one has a line not even so it's correct

Answer:

Graph A

Step-by-step explanation:

The graph of a proportional relationship is a line through the origin or a ray whose endpoint is the origin.

Graph A is the only graph that goes through the origin (the point where the x and y axis intersect).

the radius of a circle is 2 yards. what is the circles area

Answers

4pi or roughly 12.57 yd^2

Use pi r ^2 to find area

The whales' star cornerback is paid $1 million and is guaranteed a 19% pay raise for the next three years. What will his salary be three years from now?.

Answers

The income of whales star after 3 years and getting 19% rise every year will be  $1685159 .

Given, The whales' star cornerback is paid $1 million and is guaranteed a 19% pay raise for the next three years .

To get the salary of whale star after 3 years of increment with 19%.

Salary =  $1 million

Salary after 1st increment =  $1 million +  $1 million of 19%

Salary after 1st increment = $1190000

Salary after 2nd increment =  $1190000 + $1190000 of 19%

Salary after 2nd increment = $1416100

Salary after 3rd increment =  $1416100 + $1416100 of 19%

Salary after 3rd increment = $1685159

Final salary after 3 years will be  $1685159.

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15 is 20% of what number? Enter your answer in the box. ​

Answers

Answer:

75

Step-by-step explanation:

Please help!!!!!!!!!!!!!!!

Please help!!!!!!!!!!!!!!!

Answers

well if you look at it it comes at a slope

0.93=

please explain how you got the answer.

Answers

fraction form 93/100
percentage form 93%
theres many wayss you could write this but im not sure i surley understand what you mean by this question

can someone find the answer to this please asap :)​

can someone find the answer to this please asap :)

Answers

Answer:

Step-by-step explanation:

x=1 and y=1

Step-by-step explanation:

y=6x-8

3x=10-y

y=2(10-y)-8

3x=10-y

2y=12

3x=10-y

y=6

3x=4

y=6

x=4/3

The center of a circle is located at (0, 4).


What is the approximate area of the circle?

19 units

38 units

113 units

452 units


show your work

The center of a circle is located at (0, 4).What is the approximate area of the circle?19 units38 units113

Answers

The area of the circle in the graph is 113 square units.

How to find the area of the circle?

Remember that for a circle of radius R, the area is given by the simple formula you can see below.

A = pi*R²

Where pi = 3.14, so we can use this formula to find the area of the circle.

On the diagram we can see that the radius of the circle is:

R = 6 units

Replacing that in the area formula we will get.

A = 3.14*(6 units)²

A = 113.04 units ²

The correct option is the third one.

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What is the slope indicated in the table below
please help and show work!

What is the slope indicated in the table belowplease help and show work!

Answers

The slope of the table is 5 / 4 .

How to find the slope of a table?

The slope of a line is the change in the dependent variables with respect to the change in the independent variable.

The slope of a line is rise over run.

In other words, the slope of a line is a measure of its steepness.

Therefore, let's find the slope of the table.

slope = change in y / change in x

Therefore,

slope = y₂ - y₁ / x₂ - x₁

Using (4, 5) and (8, 10)

slope = 10 - 5 / 8 - 4

slope = 5 / 4

Therefore, the slope is 5 / 4.

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Answer:

1.25

Step-by-step explanation:

You divide five by four, and you get one and twenty-five hundredths.

If I read 9 pages in 18 minutes how many pages will I read in 10 minutes

Answers

The answer is 5 pages

the triangles are similar solve for x.

the triangles are similar solve for x.

Answers

Answer:

2.5

Step-by-step explanation:

12 -> 6
so the triangle on the left is dilated 2x the triangle on the right

5 -> 2.5

12 ➡️ 6

(12/2 = 6)

5/2 = X

X= 2.5

En una imprenta hacen pegatinas para discos de música de forma que se cubra la parte superior del CD. Sabiendo que el radio mayor mide 5. 8 cm y el menor 0. 7 cm aproximadamente, ¿qué área de papel utilizan para cada CD?

Answers

El área de papel utilizada para cada CD es aproximadamente 20.41 cm².

How much paper area is used for each CD?

Para calcular el área de papel utilizado para cada CD, necesitamos determinar el área de la región entre dos círculos concéntricos.

El área de un círculo se calcula utilizando la fórmula A = πr², donde r es el radio. En este caso, tenemos dos círculos con radios diferentes: el radio mayor de 5.8 cm y el radio menor de 0.7 cm.

El área del papel utilizado será la diferencia de áreas entre los dos círculos. Entonces, podemos calcularlo de la siguiente manera:

Área utilizada = Área del círculo mayor - Área del círculo menor

= π(5.8²) - π(0.7²)

= π(33.64) - π(0.49)

≈ 105.72 - 1.54

≈ 104.18 cm²

Por lo tanto, aproximadamente se utilizan 104.18 cm² de papel para cada CD.

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