Let A be a complex (or real) n x n matrix, and let x in C^n be an eigenvector corresponding to an eigenvalue (lambda) in C Show that for each nonzero complex scalar (nu) , the vector (nu) x is an eigenvector of A

Answers

Answer 1

The vector (nu) x is an eigenvector of A and corresponds to each nonzero complex scalar (nu) (lambda).

Let x in Cn be an eigenvector of A that corresponds to an eigenvalue. Assume that A is a n x n matrix (lambda). Ax = (lambda)x follows.

Let (nu) now be a complex scalar that is nonzero. A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x)

As a result, (nu)x is an eigenvector of A that corresponds to (nu) (lambda).

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Related Questions

A) how many prime numbers are multiples of 5? b) how many prime numbers are multiples of 8?.

Answers

Answers to both subparts are shown:

(A) Only 1 prime number is in the multiples of 5 which is number 5 itself.

(B) No prime numbers are in the multiples of 8.

What are prime numbers?

Any natural number higher than 1 that is not the sum of two smaller natural numbers is referred to be a prime number.

A composite number is a natural number greater than one that is not prime.

For instance, the number 5 is prime because there are only two ways to write it as a product, 1 × 5 and 5 × 1.

(A) Prime numbers that are multiples of 5:

All numbers that come in the table of 5 are multiples of 5.

Only the number 5 is the number that comes in the table of 5 is a prime number.

As 5 is only divisible by 1 and 5 itself.

(B) Prime numbers that are multiples of 8:

All numbers that come in the table of 8 are multiples of 8.

No number that comes in the table of 8 is a prime number.

As all the numbers are divided by also as 8 is an even number.

Therefore, answers to both subparts are shown:

(A) Only 1 prime number is in the multiples of 5 which is number 5 itself.

(B) No prime numbers are in the multiples of 8.

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PLEASE HELP IMMEDIATELY!!!!
Select all of the zeroes of the function.

Answers

Answer: A C and D

Step-by-step explanation:

Answer: A B

Step-by-step explanation: because I sadly had to figure it out, anyways hope this helps y'all

Hi! Please help asap!!!!!!!!!!!!!!

Answers

Answer:

the weight of a male: G+M

total weight of females: A

weight of child: G

total weight of adults: M+A

Step-by-step explanation:

i mean... u got it right

What is the equation of a line parallel to 8x+ 4y =8 and passes thru the point (2,4)? Write the equation in slope-intercept form (y=mx+b)

Answers

the answer is 9x+4y=8

Housing prices in a small town are normally distributed with a mean of $156,000
and a standard deviation of $8,000 . Use the empirical rule to complete the following statement. Approximately 99.7 % of housing prices are between a low price of$_______ and a high price of$_______

Answers

So the answer here is approximately 95% of housing prices are between a low price of  $143000 and a high price of $171000.

What is meant by empirical rule?

The empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, is a statistical principle that asserts that, with a normal distribution, virtually all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).

The empirical rule specifically states that 68% of observations will fall inside the first standard deviation, 95% will fall within the first two standard deviations, and 99.7% will fall within the first three standard deviations.

The Empirical Rule indicates that 99.7% of data that are seen to have a normal distribution fall within 3 standard deviations of the mean.

According to this criteria, 68% of the data falls within one standard deviation, 95% within two standard deviations, and 99.7% within  three standard deviations of the mean.

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H''B''G''P'' was created using a sequence of tranformation applied to HBGP, the preimage. Compleate the image below according.

Answers

The figure H''B''G''P'' created following the transformations applied to HBGP such that HBGP is larger than  H''B''G''P'', inverted and on the other side of the y-axis indicates;

The completed table is presented as follows;

[tex]\begin{array}{|c|c|c|c|c|\pi \pi }\text{Preimage} &\text{Side Length} & \text{Image} &\text{Side Length}&\text{Ratio of Preimage to Image Lengths } \\GB & 5 &G''P'' &2.5&2:1 \\PH &3 & P''H'' &1.5&2:1 \\HB & 5 & H''B'' &2.5&2:1 \\BG &3 & B''G'' & 1.5& 2:1 \\\end{vmatrix}[/tex]

What is a transformation in geometry?

A geometric transformation involves making changes to a geometric figure.

The coordinates if the vertices of the quadrilateral HBGP are;

H(-1, -2), B(-6, -2), G(-6, 1), and P(-1, 1)

The approximate coordinates of the vertices of the quadrilateral H''B''G''P'' are;

H''(0.5, 1), B''(3, 1), G''(3, -0.5), P''(0.5, -0.5)

The length of the side GP in quadrilateral HBGP = -1 - (-6_) = -1 + 6 = 5

Length of the side PH in quadrilateral HBGP = 1 - (-2) = 1 + 2 = 3

Length of the side HB in quadrilateral HBGP = -1 - (-6) = -1 + 6 = 5

Length of the side BG in quadrilateral HBGP = 1 - (-2) = 1 + 2 = 3

The possible transformations applied to HBGP to create H''B''G''P'' includes;

A dilation, a rotation of 180° and a translation

The length of the side G''P'' in quadrilateral H''B''G''P'' = 3 - 0.5 = 2.5

The length of the side P''H'' in quadrilateral H''B''G''P'' = 1 - (-0.5) = 1 + 0.5 = 1.5

The length of the side H''B'' in quadrilateral H''B''G''P'' = 3 - 0.5 = 2.5

The length of the side B''G'' in quadrilateral H''B''G''P'' = 1 - (-0.5) = 1 + 0.5 = 1.5

Ratio of the side length of GP to the side length of G''P'' = 5:2.5 = 2:1

Ratio of the side length of PH to the side length of P''H'' = 3:1.5 = 2:1

Ratio of the side length of HB to the side length of H''B'' = 5:2.5 = 2:1

Ratio of the side length of BG to the side length of B''G'' = 3:1.5 = 2:1

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The random variable x is normally distributed with mean 5 and standard deviation 25.

Answers

(C) The standard deviation is 100 and the mean is 22.

What is the standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.

While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

So, using the concepts of expected value and variance of random variables, this issue can be resolved.

By the expected value principle:

E(Y) = E(2+4X) = E(2) + E(4X) = 2 + 4E(X) = 2 + 4(5) = 22

[tex]\mathrm{E}(\mathrm{Y})=\mathrm{E}(2+4 \mathrm{X})=\mathrm{E}(2)+\mathrm{E}(4 \mathrm{X})=2+4 \mathrm{E}(\mathrm{X})=2+4(5)=22[/tex]

Then, μy = 22

In terms of variance concept:
Var(Y) = Var(2 + 4x) = Var(2) + Var(4x) + 2Cov(2, 4x)

Cov(2, 4x) = 0

Var(2) = 0

Hence:
Var(Y) = Var(4x) = 4²Var(X) = 16σ²ₓ = 16(25²) = 10000

Standard deviation(Y) = √10000 = 100

Therefore, (C) the standard deviation is 100 and the mean is 22.

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Complete question:
The random variable X is normally distributed with a mean of 5 and a standard deviation of 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y? The mean is 20 and the standard deviation is 102.

A) The mean is 20 and the standard deviation is 50.

B) The mean is 22 and the standard deviation is 102.

C) The mean is 22 and the standard deviation is 100.

D) The mean is 22 and the standard deviation is 50.

If 30% of the nucleotides in a single-stranded rna molecule are adenine, then what percent are expected to be thymine? responses 0% 0% 20% 20% 30% 30% 70%.

Answers

Answer:

70%

Step-by-step explanation:

the percentage of both single stranded RNA molecule which are adenine and thymine is 100%

the Perce of the adenine is 30

therefore, 100 - 30=70

Find the missing value for the exponential function represented by the table below.
X
-2
-1
0
1
2
y
29
20.3
14.21
6.9629
Then select the graph that best fits the equation.
a) -9.947, graph a
b) 9.213, graph b
c) 9.947, graph a
d) 8.756, graph b

THE ANSWER IS C) 9.947, graph A

i couldn't find the right answer anywhere in here so im giving it

Answers

Answer:THE ANSWER IS C) 9.947, graph A

;)

Step-by-step explanation:

an exam is given to students in an introductory statistics course. what is likely to be true of the shape of the histogram of scores if the exam is quite easy?

Answers

If the exam is quite easy then the shape of the histogram would be negatively skewed.

What is a histogram?

A histogram is a statistical information display that uses rectangles to show the frequency of data items in equal-sized numerical intervals. The independent variable is plotted along the horizontal axis and the dependent variable is plotted along the vertical axis in the most common form of a histogram.

a) If the exam is quite easy, it is expected that the majority of the students score well on the test, and since most of the data is closer to the maximum value rather than the minimum, the histogram has a negatively skewed shape.

Hence, if the exam is quite easy then the shape of the histogram would be negatively skewed.

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if the distance traveled is 40 miles and thee time it took is 2 hours what is the average speed?

Answers

Answer:

20mph

Step-by-step explanation:

Answer:

20 mph

Step-by-step explanation:

I used my own work and double-checked it with a calculator.

A 99% confidence interval for the ratio of two population standard deviations (sigma_1/sigma_2) ranges from 1.06 to 2.22. Based on this confidence interval,
a. We can not make any meaningful statement about the difference between two population standard deviations.
b. We can conclude that sigma_1 is larger than sigma_2.
c. We can not conclude that there is a significant difference between the two population standard deviations. d. We could conclude that the sgima_2 is larger than the sigma_1.

Answers

A 99% confidence interval for the ratio of two population standard deviations (sigma_1/sigma_2) ranges from 1.06 to 2.22. Based on this confidence interval, we can conclude that sigma_1 is larger than sigma_2. (Option B).

A confidence interval (CI) refers to a range of estimates for an unknown parameter. A confidence interval for a standard deviation refers to the range of values that is likely to contain a population standard deviation with a certain level of confidence. In the given situation, when sigma 1 is divided by sigma 2, the result lies within the range from 1.06 to 2.22. When a number x is divided by number y, the result would be less than 1 if x < y, greater than 1 if x > y, and equal to 1 if x = y. Since the ratio of sigma 1 and sigma 2 is more than 1, sigma 1 is greater than sigma 2.

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You jog 2 kilometers in 12 minutes. Your friend jogs 3 kilometers in 16.5 minutes. Who jogs faster? The faster jogger will finish a five-kilometer race____
minutes sooner than the slower jogger.

Answers

Answer:

Your friend jogs faster and he will finish a 5 km race in 27.5 minutes

You jog 1km every 6 minutes and your friend jogs 1km in 5.5 minutes

Step-by-step explanation:

Redbox has two video rental plans. The standard plan charges $3.25 for each video rental. The premium video rental has an $8.75 membership fee and charges $2 per rental. At how many rentals do the plans cost the same?

Answers

Answer:

Your answer is 7 rentals, at the cost of $22.75.

Step-by-step explanation:

First, let's make an equation

[tex]y =[/tex] total cost while [tex]x=[/tex] amount of rentals

[tex]y = 3.25x[/tex]

[tex]y = 2x + 8.75[/tex]

After graphing the two, we find that they intersect and 7, 22.75

Hence, the answer is 7 rentals, at the cost of $22.75

Виконати дії 3/7*2/15

Answers

Answer: 16

Step-by-step explanation:

its 16 because if you do 3/7 times 2/15 it gives you 16

Answer: x = 37

Step-by-step explanation: (3/7)*(x-2) = 15 // - 15

(3/7)*(x-2)-15 =

0 3/7*(x-2)-15 = 0

3/7*(x-2)-15 = 0

3/7*x-111/7 = 0

3/7*x-111/7 = 0 // + 111/7

3/7*x = 111/7 // : 3/7

x = 111/7/3/7

therefore the answer is x =37

a sample of 49 parents found the mean time spent posting pictures of their children on social media per week was 19 minutes with a standard deviation of 3.9 minutes. find the p-value used to test a claim that the mean time parents spend posting pictures of their children per week is more than 18 minutes at the 5% significance level.

Answers

The p-value will be 0.9457

Sample size = 49

Meantime = 19 minutes

Standard deviation = 3.9 mins

Calculating the z-score for test statistic -

z = (x - μ) / (s / √n)

z = (19 - 18) / (3.9 / √49)

= 1 / 0.63

= 1.58

To find the p-value, we can use a standard normal table to find area under the normal curve of the z-score.

The p-value will be the area under the curve to the right of 1.58.

This value is 0.9457, which means that there is a 94.57% chance.

Now,

Since the p-value is greater than the significance level (0.9457 > 0.05),  the null hypothesis can not be rejected. Therefore, the mean time parents spend posting pictures of their children per week is not significantly different from 18 minutes at the 5% significance level.

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Which postulate or theorem proves △MNQ≅△PNQ?


​SSS Congruence Postulate​ ​

SAS Congruence Postulate

AAS Congruence Theorem

ASA Congruence Postulate

Answers

Answer:

ASA

Step-by-step explanation:

angle side angle because, due to vertical angles, the outer angles of both triangles are congruent, and the middle side is reflexive property

hope this helps :3

Please help now asap !!!!!!!!!!!!!!!!!

Answers

Answer:

15 is a composite number.

What are all composite number?

In basic Mathematics, the numbers that have more than two factors are known as composite numbers. For example, factors of 6 are 1, 2, 3 and 6. Thus, there are four factors in total, and 6 is a composite number. The first ten composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18. To understand better, have a look at the following examples.

Therefore, your answer is 15

determine the force in each member of the space truss and state if the members are in tension or compression. hint: the support reaction at e acts along member eb. why?

Answers

An arrangement of bars joined at the ends to create a two- or three-dimensional structure is called a truss.

External forces and responses to those forces are thought to act only at the nodes and cause either tensile or compressive forces in the members.

A planar truss is a two-dimensional truss that has all of its members and forces in the same plane. A space truss is another name for a three-dimensional truss. A member is said to be in traction when it is being pulled or pushed. When a member is being pushed or pulled, it is said to be in compression, and when it is in tension.

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Given δxyz ≅ δegf, find the measurements of the unknown sides and angles. zx = in. eg = in. m∠x = ° m∠g = °

Answers

The measure of the given sides and angles are,

1) ZX = 1.3 inch

2) EG = 3.0 inch

3) m ∠ X = 48°

4) m ∠G = 25°

What is congruent triangles?

If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.

Given: ΔXYZ ≅ ΔEGF

Because the triangles are assumed to be congruent, their corresponding angles and sides must have similar measurements and lengths.

a. ZX = _ in

ZX's length is the same as FE's length. Therefore, the length should be 1.3 inches.

b. EG = _ in

EG's length is the same as XY's length. The figure indicates that the answer should be 3.0 in.

c. m ∠X = _ °

Angle E and angle x should both have the same measure. This is stated to be 48 degrees.

d. m ∠G

Angle Z's measurement is the same as angle F's measurement.

In that case, 107° should be the value assigned to angle F.

Angle E in the triangle to the right measures 48°, while angle F measures 107°.

the sum of these angles is subtracted from 180°.

The angle G's measure, which is equal to 25°.

Hence,

1) ZX = 1.3 inch

2) EG = 3.0 inch

3) m ∠ X = 48°

4) m ∠G = 25°

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Complete question:

Complete question is attached below.

The ide of a rectangular garden at 20 feet and 15 feet. If each ide of the garden i increaed by 25% find the percentage of the rea

Answers

Answer:

The percentage of area increased is 56.25%

Step-by-step explanation:

What is Area ?

Area is the total amount of space occupied by a flat (2-D) surface or an object's shape.

Length of the garden = 20 feet

Breadth of the garden = 15 feet

Area of Original rectangular garden  = 20 × 15 = 300 [tex]feet^{2}[/tex]

If each side is increased by 25%

Then,

Length of new garden = 20 + [tex]\frac{25}{100}[/tex]×20 = 25 feet

Breadth of new garden = 15 +[tex]\frac{25}{100}[/tex]×15  =18.75 feet

Area of new rectangular garden = 25×18.75 =468.75[tex]feet^{2}[/tex]

Increase in Area = (468.75-300) [tex]feet^{2}[/tex]

                            =  168.75 [tex]feet^{2}[/tex]

Percentage of area increased = [tex]\frac{168.75}{300}[/tex]×100= 56.25%

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A rectangle has an area of 104 square centimeters and a width of 8 centimeters. What is the perimeter?

13 centimeters
26 centimeters
34 centimeters
42 centimeters

Answers

Answer:

[tex]\huge\boxed{\sf P = 42 \ cm}[/tex]

Step-by-step explanation:

Given:Area = 104 cm²Width = 8 cmFormulas to be used:Area = Length × WidthPerimeter = 2Length + 2WidthSolution:

Finding length:

Area = Length × Width

104 = Length × 8

Divide 8 to both sides

104/8 = Length

13 cm = Length

Length = 13 cm

Finding Perimeter:

P = 2Length + 2Width

P = 2(13) + 2(8)

P = 26 + 16

P = 42 cm

[tex]\rule[225]{225}{2}[/tex]

Point A lies at 6 on an number line and is dilated using
the origin as the center with scaling factor of 5/2. At
what location does its image lie on the number line?
O 18
O 15
O22
25

Answers

Point A will lie at the point 15 on the number line.

What is dilation?

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape. A dilation should either stretch or shrink the original shape. This transformation is expressed by the term “scale factor.”

If point A is at 6 and it is dilated by the factor 5/2 which means extension then the new location of point A is 5/2 x 6 which is 15

In conclusion the new location of point A on the number line is 15

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A light year is equivalent to 6.7x10^8 miles/hour. If my house is 34700 meters from school, how many seconds would it take me to get to school if I drove at the speed of a light year?

Answers

If I drove at the speed of a light year it would take me 1.152×10⁻⁴ seconds.

What is scientific notation?

In scientific notations numbers are written in the form of a base that is

0  ≤ b < 10 and multiplied by 10ⁿ where n represents integers.

We write large standard numbers in the scientific form in a compact manner.

We know 1 meter is 0.000621371 miles.

∴  34700 meters is (34700× 0.000621371) = 21.56 = 2.156×10¹ miles.

Given, A light year is equivalent to 6.7x10^8 miles/hour.

∴ It would take (2.156×10¹/6.7x10^8) = 0.32×10⁻⁷ miles per hour.

Or (0.32×10⁻⁷×3600) = 1.152×10⁻⁴ seconds.

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I WILL OPEN MY ALT AND COMENT AND GIVE YOU A BRINLIST OPEN IF YOU SHOWED YOUR WORK!!! OPEN THE IMAGE

Answers

Solve for n by simplifying both sides of the equation, then isolating the variable.

n = 1


Answer:

n = 1

Step-by-step explanation:

1. Combine multiplied terms into a single fraction

2. Find common denominator

3. Combine fractions with common denominator

4. Combine multiplied terms into a single fraction

5. Multiply by 1

6. Multiply the numbers

7. Rearrange Terms

8. Add n to both sides

9. Simplify

10. Multiply all terms by the same value to eliminate fraction denominators

11. Cancel multiplied terms that are in the denominator

12. Subtract 2 from both sides

13. Simplify

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 9 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

A couch and coffee table cost a total of $1140. The cost of the couch is two times the cost of the coffee table. Find the cost of each item

Answers

Answer:

coffee table = 380

couch = 760

Step-by-step explanation:

1140÷3=380

table= 380×1=380

couch = 380×2=760

A group of friends wants to go to the amusement park. They have no more than $150 to spend on parking and admission. Parking is $15.50, and tickets cost $19.25 per person, including tax. What is the maximum number of people who can go to the amusement park?

Answers

Answer: Maximum amount of people who can go to the amusement park is 6

Step-by-step explanation:

Answer:

Just add 15.50+19.25 several times until you reach 150 or 150+

therefore, The max amount of friends would be 4. This is because 15.50x4= 62 and 19.25x4=77. 77+62=139. If you went any farther up you would get more than 150, passing the budget.

Barry's final score is 45 which player had the greater final score?

Answers

The player with the greater final score is of:

Barry.

How to obtain which player had the greater final score?

Barry's final score is given as follows:

45.

Then we have to obtain Lee's score, from the description given in the missing information section.

Lee's scored is obtained as follows:

Starts at -350.Answers a 275-point question correctly, hence - 350 + 275 = -75.Answers a 70 - point question correctly, hence -75 + 70 = -5.Answers a 50 - point question incorrectly, hence: -5 - 50 = -55.

Thus Lee's final score is given as follows:

-55.

The classifications of the final scores according to the signals are given as follows:

Barry: positive score.Lee: negative score.

A positive score will always be greater than a negative score, hence Barry had the greater final score.

Missing information

Lee and Barry play a trivia game in which questions are worth different numbers of points. If a question is answered correctly, a player earns points. If a question is answered incorrectly, the player loses points. Lee currently has -350 points.

a. Before the game ends, Lee answers a 275 -point question correctly, a 70 -point question correctly, and a 50 -polnt question incorrectly. Write and find the value of an expression to find Lee's final score.

b. Barry's final score is 45. Which player had the greater final score?

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100 points need answer asap!!
y=x-7
y=x+7
solve for x and y

Answers

Answer:7 sry if this is not correct but that is the answer

Step-by-step explanation:

x=7-y             y-x=7

2y-7=7          x= 7-y

y=7              x=7-y

x=0              y=7

x= 7

here is  your answer

How can you tell that 5/8 is a terminating decimal but 5/9 is a repeating decimal?

Answers

look at my glorious answer mah boi

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