In Exercises 1, 2, 3, 4, 5, and 6, show that v is an eigenvector of A and find the corresponding eigenvalue. A= [ -1 16 0 ] V = [1 -2]
Answers
Av = λv, so we can conclude that v is an eigenvector of A and the corresponding eigenvalue is λ = -2.
A*v = [-1 16 0] * [1 -2] = [-1 -32 0]
λv = [-2 -4 0]
Since Av = λv, we can conclude that v is an eigenvector of A and the corresponding eigenvalue is λ = -2.
1. First, we multiply the matrix A with vector v to find the product Av.
2. A*v = [-1 16 0] * [1 -2] = [-1 -32 0]
3. Then, we multiply the eigenvalue λ with vector v which gives the result λv.
4. λv = [-2 -4 0]
5. We compare Av and λv. If they are equal, then v is an eigenvector of A and the corresponding eigenvalue is λ.
6. Av = λv, so we can conclude that v is an eigenvector of A and the corresponding eigenvalue is λ = -2.
Learn more about eigenvector here
https://brainly.com/question/13050052
#SPJ4
Related Questions
Compare the corresponding vertices in problem 2 and identify the transformation that produced LMN FROM ABC
Answers
Answer:
“The Beginnings of the Maasai.”
These cattle are sacred, bec
Step-by-step explanation:
Which equation represents the transformed function below?
On a coordinate plane, 2 functions are shown. The parent function starts at (0, 0) and then curves up in quadrant 1. The transformed function starts at (negative 2, 0) and then curves up into quadrant 1.
_____ = parent function; y = StartRoot x EndRoot
- - - - - = transformed function
y = StartRoot x + 2 EndRoot
y = StartRoot x EndRoot + 2
y = StartRoot x EndRoot minus 2
y = StartRoot x minus 2 EndRoot
Answers
The translated function can be written as:
y = √(x + 2)
Which equation is the transformed function?Here we know that the parent square root function is:
f(x) = √x
It passes through the point (0, 0) and opens to the right side.
The transformed function is similar, but it starts at (-2, 0)
So we had a translation of 2 units to the left.
Remember that for any function y = f(x) an horizontal translation of N units to the left is written as:
y = f(x + N)
Here we will have:
y = f(x + 2) = √(x + 2)
y = √(x + 2)
Learn more about translations at:
https://brainly.com/question/24850937
#SPJ1
Answer:
A
Step-by-step explanation:
y=\(\sqrt{x+2\)
Explain your answer to the question in the picture with steps please, thank you.
Answers
Part (a)
Answer: Constant of proportionality = 5/8
Reason:
The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.
The direct proportion line must pass through the origin. In other words, the y intercept must be zero.
=====================================
Part (b)
Answer: Not Proportional
Reason:
The y intercept isn't zero.
Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.
Of all the soft drink consumers in a particular sales region, 30% prefer Brand A and 70% prefer Brand B. Of all these soft drink consumers, 20% prefer Brand A and are female, and 40% prefer Brand B and are female. What is the probability that a randomly selected consumer is female, given that the person prefers Brand A? A. 0.18 B. 0.21 C. 0.34 D. 0.67
Answers
Answer:
The answer to this question should be D. 0.67
Hope this helped.
(a) Show that if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^{T}\). Show with an example that the eigenvectors of A and \(A^{T}\) are not the same.
(b) Show that if λ is an eigenvalue of A, and A is invertible, then λ^-1 is an eigenvalue of A^-1.
Answers
If λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.
What are eigenvalues and eigenvectors?The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.
The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.
Then, we have:
Av = λv
Taking transpose on both sides we have:
\(v^T A^T = \lambda v^T\)
The above equations thus relates transpose of vector and transpose of A to λ.
Now, consider a matrix:
\(\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]\)
Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.
The eigenvectors are:
\(v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T\)
Now, for transpose of A:
\(A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right]\)
The eigen vectors are:
\(u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T\)
Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.
Learn more about eigenvalues here:
https://brainly.com/question/29749542
#SPJ1
A bag of marbles has 12 green marbles, 5 red marbles, 8 blue marbles and 7 yellow marbles. What is the probability of randomly selecting a blue marble?
Answers
Probability = # of desired options / # of total options
Our desired option is blue and there are 9 blue marbles in the bag.
There are 32 total marbles (options) in the bag.
P(blue) = 9 / 32 = 0.28125 = 28.125%
Hope this helps!
Determine if the pairs of expressions below are always equivalent. Prove your answer
A. 4n + 12 and 4 (n +3)
B. m + m 3m and 3m + 2
C. 4x + 8y and 4 (x + 8y)
D. 3 (2t + 2 ) and ( t + 1 ) x 6
E. p + p and p + 7
Answers
Find the missing number in the following fraction calculation
/7 ÷10 =3/35
Answers
x=6
Step-by-step explanation:
x ÷ 7 ÷10 = 3/35
(Use trial & error - since I knew x<7)
6/7 ÷ 10 = 3/35
Or
3/35 x 10
(then, simplify it to 6/7 or ÷ that by 1/7 to get 6)
Hope this helps!
Simplify to a single power of 5:
(5^4)^3
Answers
Answer:
5^12
Step-by-step explanation:
This is called the "Power of Powers rule." When you are doing this rule, the inside exponent inside the parenthesis (the ^4 in this case) multiplies with the one outside the parenthesis, like this: 5^4*3 = 12.
However, if there is a base number next to the exponent outside the parenthesis that is a different number than the one inside the parenthesis, this method will not work. (Example: (5^4)5^3)
Important note: Anytime you are combining exponents through any rule, the base number must be the same to be able to combine.
If you deposit $2000 in an account earning 3% interest compounded monthly, how much will you have in the account in 20 years?
Answers
What is the equation of the line that passes through the point (-6, -2) and has a
slope of -1/6?
Answers
The equation of the line that passes through the point (-6, -2) and has a slope of -1/6 will be y = -(1/6)x - 3.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope is - 1/6. Then the equation is given as,
y = -1/6 x + c
The equation passes through (-6, -2). Then we have
-2 = - (1/6) (-6) + c
- 2 = 1 + c
c = - 3
Then the equation is given as,
y = - (1/6)x - 3
The equation of the line that passes through the point (-6, -2) and has a slope of -1/6 will be y = -(1/6)x - 3.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
If given the endpoints of a line segment, is this enough information to write the equation of a circle?
Answers
Answer:
not really no not for me
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answers
Answer:
x = 1 , x = 13
Step-by-step explanation:
(x - 7)² = 36 ( take square root of both sides )
x - 7 = ± \(\sqrt{36}\) = ± 6 ( add 7 to both sides )
x = 7 ± 6
then
x = 7 - 6 = 1
x = 7 + 6 = 13
Find the remainder when 5^400 is divided by 19
Answers
Answer:
the remainder is 0
Step-by-step explanation:
There is a 22% chance it will rain tomorrow and a 6% chance of strong winds. What is the chance it will stay dry
Answers
Answer:
72% if I get it wrong then I'm really sorry
Step-by-step explanation:
Use an area model to solve the
expression 0.6 × 0.4. (6-4)
Answers
Step-by-step explanation:
the answer is 48 because
What is the area of a water bottle if the base is 6cm
Answers
The quantity of the water in the water bottle is 648ml
How did we get the value?Find the area,
Area of the bottle = 6 x 6
= 36cm²
To determine the quantity of the water in the bottle, multiply the area by the level of the water in the bottle:
area of the bottle x level of the water
= 36 x 18
= 648cm
When you convert it to ml, it becomes 648ml
learn more about area: https://brainly.com/question/2607596
#SPJ1
The complete question goes thus:
A water bottle has a square base of side 6 cm . If the bottle is filled up to a height of 18 cm .How much water is in the water bottle ?
Hi, can you help me answer this question please, thank you!
Answers
A U.S. government survey in 2007 said that the proportion of young Americans that earn a high school diploma is 0.87. a) Suppose you took a simple random sample of 100 young Americans. We know because of sampling variability that the sample proportion of those who earned a high school diploma would vary each time you took a sample. Assuming the value above can be taken as the population proportion (i.e. as a parameter), what model can be used to describe how these sample proportions would vary? Please be sure to include the name of the distribution and the parameter values. b) Find the probability that 89% or more in the sample will have earned a high school diploma.
Answers
The probability that 89% or more in the sample will have earned a high school diploma is p ~ N = ( 0.87 , 0.001131 )
The normal distribution can be used to model the sample proportions.
The Central Limit Theorem and the importance of the normal distribution model in statistics (CLT). According to this theory, regardless of the type of distribution, the variables are sampled from, averages calculated from independent, identically distributed random variables have approximately normal distributions (provided it has finite variance).
Given,
N ( sample size ) = 100
probability of earning a high school diploma (p) = 0.87
probability of not earning a high school diploma ( q ) = 0.13
hence ;
∈( P ) = p = 0.87
Var ( p ) = \(\frac{pq}{n}\) = \(\frac{0.86*0.13}{100}\) = 0.001131
therefore ; p ~ N = ( 0.87 , 0.001131 )
To know more about probability visit:brainly.com/question/11234923
#SPJ4
Complete the two-way frequency table.
Type of Fruit
Food
Vegetable
Total
Child
15.5%
44.4%
%
Age
Adult (18+)
28.9%
55.6%
%
Total
57.8%
%
%
Answers
The values in the missing places are 26, 52, 14, 40 and 50
What is a frequency table?A table drawn up to show the distribution of the frequency of occurrence of a given characteristic according to some specified set of class intervals.
Given is a frequency table with some missing places,
For every missing places, we just need to add or subtract from the total.
Types of food Age
child adult (18+) Total
Fruit 26 26 52
Vegetable 14 24 38
Total 40 50 90
First missing place = 50-24 = 26
Second missing place = 26+26 = 52
Third missing place = 38-24 = 14
Fourth missing place = 26+14 = 40
Fifth missing place = 90-40 = 50
Hence, The values in the missing places are 26, 52, 14, 40 and 50
Learn more about frequency table on https://brainly.com/question/28931302
#SPJ1
Solve this equation 1/4 x 10?
Answers
Answer: 2.5
Step-by-step explanation:
Answer:
2.5
Step-by-step explanation:
Have a great day :)
Mrs. Allison buys Gucci bags wholesale for 28.00 and marks them up 900% to sell on her de online store, what is the selling price of the bags
Answers
Answer:
$288
Step-by-step explanation:
what is 900% of 28?
x = 9 × 28
x = 288
6(3x+12-4x)=2x+2+3x solve for x
Answers
Answer:
its 70/11 or 6.36
Step-by-step explanation:
What is the meaning of conditionally promoted in school
Answers
A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds. Assume that the sample is taken from a large population and the correction factor can be ignored. Round your final
answer to four decimal places and intermediate z-value calculations to two decimal places
Answers
The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:
0.5874 = 58.74%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).The parameters for this problem are given as follows:
\(\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953\)
The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem:
\(Z = \frac{X - \mu}{s}\)
Z = (18.1 - 17.2)/0.3953
Z = 2.28
Z = 2.28 has a p-value of 0.9887.
Z = (17.1 - 17.2)/0.3953
Z = -0.25
Z = -0.25 has a p-value of 0.4013.
Hence:
0.9887 - 0.4013 = 0.5874 = 58.74%.
More can be learned about the normal distribution at https://brainly.com/question/25800303
#SPJ1
In triangle ABC, AP is an angle bisector of angle BAC. What is the length of PC? Round you answer to the nearest whole number.
A) 6
B) 7
C) 8
D) 9
Answers
The length of PC is 6
Sure hope this helps you :D
Answer:
D
Step-by-step explanation:
the angle bisector divides the opposite side into segments that are proportional to the other 2 sides.
note that BP = 16 - PC , then
\(\frac{BP}{PC}\) = \(\frac{AB}{AC}\) ( substitute values )
\(\frac{16-PC}{PC}\) = \(\frac{8}{10}\) = \(\frac{4}{5}\) ( cross- multiply )
4 PC = 5(16 - PC) ← distribute parenthesis
4 PC = 80 - 5 PC ( add 5 PC to both sides )
9 PC = 80 ( divide both sides by 9 )
PC = 8.888... ≈ 9 ( to the nearest whole number )
The difference is
Of -1 -5
Answers
Answer:
-6
Step-by-step explanation:
-1 + -5 = -6
-1 - 5 = -6
Ron made 2/3 of a quart of hot chocolate. Each mug holds 1/3 of a quart. How many mugs will Ron be able to fill?
Answers
Answer: 2 mugs
Step-by-step explanation: If we divide 2/3 by 1/3 we multiply by the reciprocal
2/3 x 3/1
the threes cancel and you are left with two
= two mugs
Geometric sequences
*Each number is 4 less than 3 times the previous numbers*
A. Starting with the number 10, build a sequence of 5 numbers.
B. Starting with the number 1, build a sequence of 5 numbers.
C. Select a different starting number and build a sequence of 5 numbers.
Answers
Formula for the term of a geometric sequences has been defined as,
"Each number is 4 less than 3 times the previous numbers"
Therefore, recursive formula will be,
\(T_n=3(T_{n-1})-4\)
Now we will use this formula to build the sequence,
A). If \(T_1=10\),
Then \(T_2=3(10)-4=26\)
\(T_3=3(26)-4=74\)
\(T_4=3(74)-4=218\)
\(T_5=3(218)-4=650\)
Therefore, the sequence will be,
\(10,26,74,218,650\)
B). If \(T_1=1\),
Then \(T_2=3(1)-4=-1\)
\(T_3=3(-1)-4=-7\)
\(T_4=3(-7)-4=-25\)
\(T_5=3(-25)-4=-79\)
Therefore, the sequence will be,
\(1,-1,-7,-25,-79\)
C). If, \(T_1=5\),
Then, \(T_2=3(5)-4=11\)
\(T_3=3(11)-4=29\)
\(T_4=3(29)-4=83\)
\(T_5=3(83)-4=245\)
Therefore, the sequence will be,
\(5,11,29,83,245\)
Learn more,
https://brainly.com/question/11266123
(b) A shopkeeper gave a bill to a customer. The bill was in two digits but was mistakenly interchanged thereby undercharging the customer by $45.00. If the sum of the digits is 9, find the actual value of the bill.
Answers
The actual value of the bill can either be $90 or $81 or $18 or $54 or $27 or $72 or $36 or $63 bill.
A digit is a part of a set that, when taken as a whole, makes up a numeration system. A digit is a number in that particular circumstance. The members of the set 0 through 9 make up the digits of the decimal (base-10) Arabic numbering system.
The bill of the customer was mistakenly interchanged by $45.
The sum of the two digits of the bill is 9.
Now,
9 = 9 + 0 or,
9 = 8 + 1 or,
9 = 1 + 8 or,
9 = 5 + 4 or,
9 = 2 + 7 or,
9 = 7 + 2 or,
9 = 3 + 6 or,
9 = 6 + 3
Therefore, $45 bill can be mistakenly interchanged by $90 or $81 or $18 or $54 or $27 or $72 or $36 or $63 bills.
Learn more about bill here:
https://brainly.com/question/16405660
#SPJ9