Let λ be an eigen value of an invertible matrix. Then, [tex]\lambda^{-1}[/tex] is surely an eigenvalue of [tex]A^{-1}[/tex].
What is an invertible matrix?
For a matrix to be invertible, it must have a unique matrix that, when multiplied with the original matrix, gives the identity matrix.
[tex]A * B = B * A = I[/tex]
Suppose A is an invertible matrix and λ is an eigenvalue of A with a corresponding nonzero eigenvector x, i.e., Ax = λx.
To show that [tex]\lambda^{-1}[/tex] is an eigenvalue of [tex]A^{-1}[/tex], we need to find a nonzero vector y such that [tex]A^{-1}y[/tex] = [tex]\lambda^{-1}y[/tex].
Let's start by multiplying both sides of the equation Ax = λx by [tex]A^{-1}[/tex]:
[tex]A^{-1}(Ax) = A^{-1}(\lambda x)[/tex]
(x is nonzero, so we can divide by x)
[tex]A^{-1}(Ax/x) = A^{-1}(\lambda x/x)\\A^{-1}(A(x/x)) = A^{-1}(\lambda)[/tex]
Since [tex]A^{(-1)}A = I[/tex] (identity matrix), and x/x = 1, we have:
[tex]A^{(-1}(I) = A^{(-1)}[/tex] λ
[tex]A^{(-1)}[/tex] = λ[tex]A^{(-1)}[/tex]
Now, let y = A^(-1)x. We can rewrite the equation above as:
[tex]A^{(-1)}x[/tex] = λ[tex]A^{(-1)}y[/tex]
([tex]A^{(-1)}x[/tex]/λ) = [tex]A^{(-1)}y[/tex]/λ
(x is nonzero, so we can divide by x)
([tex]A^{(-1)}x/x[/tex])/λ = [tex](A^{(-1)}y/y[/tex])/λ
([tex]A^{(-1)}(x/x)[/tex])/λ = ([tex]A^{(-1)}y/y[/tex])/λ
([tex]A^{(-1)}(1)[/tex])/λ = ([tex]A^{(-1)}y/y[/tex])/λ
([tex]A^{(-1)}[/tex])/λ = ([tex]A^{(-1)}y[/tex])/λ
Since [tex]A^{(-1)}[/tex] is a matrix and λ is a scalar, we can rearrange the equation as follows:
([tex]A^{(-1)}[/tex])/λ = [tex]A^{(-1)}[/tex]y/λ
(1/λ)[tex]A^{(-1)}[/tex] =[tex]A^{(-1)}[/tex]y/λ
This shows that 1/λ is an eigenvalue of [tex]A^{(-1)}[/tex] with the corresponding eigenvector y. Therefore, we have shown that if λ is an eigenvalue of A, then [tex]\lambda^{(-1)}[/tex] is an eigenvalue of [tex]A^{(-1)}[/tex]
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se desea constrir una barda utilizando block . las dimensiones de la barda son 25 m de largo y 2 m de altura . si se requieren 12 blocks para cada metro cuadrado de barda ¿ cuantos blocks se usaran en su construcción?
respuesta urgente !!!
Answer:
I don't understand the language
Step-by-step explanation:
am not form Paris
Help? I don’t understand this math
Answer:
Option J:[tex] {x}^{3} {y}^{3} [/tex]
Step-by-step explanation:
Given,
Width of the rectangular prism
= x
Length of the rectangular prism
[tex] = {x}^{2} y[/tex]
Height of the rectangular prism
[tex] = {y}^{2} [/tex]
Therefore,
Volume of the rectangular prism
= Width × Length × Height
[tex] = x \times {x}^{2} y \times {y}^{2} [/tex]
[tex] = {x}^{3} {y}^{3} [/tex]
Hence,
The required volume of the rectangular prism is
Option J:
[tex] {x}^{3} {y}^{3} [/tex]
At a certain school, 8/9 of the students are boys. Today, 2/5 of the boys brought their lunch. What fraction of the students are
boys who brought their lunch today?
Answer:
the answer is I think 2/3
Fraction of boys brought lunch today is 16/25.
Here,
Given that:
The ratio of boys at certain school = 8/9
And 2/5 of boys brought lunch today
We have to find fraction of boys brought lunch today.
What is fraction?
Fractions denote the parts of a whole or collection of objects.
Now,
The ratio of boys at certain school = 8/9
And 2/5 of boys brought lunch today
Since, the ratio of boys 8/9 denotes 8 boys out of 9 students
Therefore, number of boys = 8
Thus, Fraction of boys brought lunch today = 8 x 2/5
= 16/25
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Mhanifa can you please help me with this? It’s due ASAP! Look at the picture attached. I will mark brainliest!
Answer:
8) 76°9) 88°Step-by-step explanation:
Sum of exterior angles of any polygon is 360°Exercise 8Sum of given angles:
2x + 60° + 64° + 36° + 48° = 360°2x + 208° = 360°2x = 360° - 208°2x = 152°x = 76°Exercise 9Sum of given angles:
x + 90° + 109°+ 73° = 360°x + 272° = 360°x = 360° - 272°x = 88°Select all the expressions that have a value 10
A guacamole recipe calls for 28 ounces of peeled and seeded avocadoes. The total cost of the tomatoes is $_____ if the as-purchased unit cost of Avocado's is $1.21 per pound and the yield percentage is 72%.
The total cost of seeded avocadoes is $1.52 (approx).
Given data:
As-purchased unit cost of avocado = $1.21 per pound
Yield percentage = 72%
Convert the given quantity of avocadoes into pounds.
1 ounce = 1/16 pounds28 ounces = (28/16) pounds= 1.75 pounds
Find out the cost of 1 pound of avocado
As per the given data, the as-purchased unit cost of Avocado's is $1.21 per pound.
Find out the cost of 1.75 pounds of avocado= (1.75 x 1.21) dollars= $2.1175.
Calculate the yield amount.
After calculating the yield percentage, we can find the amount of avocado we can use after we remove the peel and seed.
Yield amount = (yield percentage × amount as purchased)/100Yield amount
= (72 × 1.75) / 100= 1.26 pounds.
Find out the cost of yield amount
Cost of yield amount = (cost of 1.75 pounds of avocado × yield amount)/1.75
Cost of yield amount = ($2.1175 × 1.26) / 1.75
Cost of yield amount = $1.5246
Hence, the total cost of 28 ounces of peeled and seeded avocadoes is $1.52 (approx).
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Given \triangle DEF△DEF triangle, D, E, F, find DE
Round your answer to the nearest hundredth.
Answer:
x ≈ 36.09
Step-by-step explanation:
Complete question
Use △DEF, shown below, to answer the question that follows: Triangle DEF where angle E is a right angle. DE measures x. DF measures 55. Angle D measures 49 degrees. What is the value of x rounded to the nearest hundredth? Type the numeric answer only in the box below.
According to the diagram
m<E = 90 degrees
m<D = 49 degrees
DF = 55 = hypotenuse
DE = x = adjacent
EF = opposite
According to SOH CAH TOA identity;
Cos theta = adj/hyp
Cos m<D = DE/DF
Cos 49 = x/55
x = 55cos49
x = 55(0.6561)
x = 36.0855
x ≈ 36.09 (to the nearest hundredth)
Answer:
x ≈ 36.09
correct on khan
Step-by-step explanation:
build a binary search tree for the words banana, peach, apple, pear, coconut, mango, and papaya using alphabetical order.
To build a binary search tree using alphabetical order for the given words, we start with an empty tree and insert each word in the appropriate position based on its alphabetical order.
Here's the step-by-step process:
Start with an empty tree.
Insert the first word, "banana," as the root of the tree.
Insert the second word, "peach," comparing it to the root. Since it comes after "banana," it becomes the right child of the root.
Insert the third word, "apple." Comparing it to the root, it comes before "banana," so we traverse to the left child of the root. Since the left child is empty, "apple" becomes the left child of "banana."
Insert the fourth word, "pear." Comparing it to the root, it comes after "banana," so we traverse to the right child. Comparing it to "peach," it comes before "peach," so we traverse to the left child of "peach." Since the left child is empty, "pear" becomes the left child of "peach."
Insert the fifth word, "coconut." Comparing it to the root, it comes before "banana," so we traverse to the left child. Comparing it to "apple," it comes after "apple," so we traverse to the right child. Comparing it to "pear," it comes before "pear," so we traverse to the left child of "pear." Since the left child is empty, "coconut" becomes the left child of "pear."
Insert the sixth word, "mango." Comparing it to the root, it comes after "banana," so we traverse to the right child. Comparing it to "peach," it comes before "peach," so we traverse to the left child. Comparing it to "pear," it comes after "pear," so we traverse to the right child. Comparing it to "coconut," it comes after "coconut," so we traverse to the right child. Since the right child is empty, "mango" becomes the right child of "coconut."
Insert the seventh word, "papaya." Comparing it to the root, it comes after "banana," so we traverse to the right child. Comparing it to "peach," it comes after "peach," so we traverse to the right child. Comparing it to "pear," it comes after "pear," so we traverse to the right child. Comparing it to "coconut," it comes after "coconut," so we traverse to the right child. Comparing it to "mango," it comes after "mango," so we traverse to the right child. Since the right child is empty, "papaya" becomes the right child of "mango."
The resulting binary search tree will look like this:
banana
/ \
apple peach
\ \
pear papaya
/
coconut
\
mango
Note: The tree might have different structures depending on the order of insertion, as long as it maintains the binary search tree property.
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Aubrey has a new art box in the shape of a rectangular prism. The box is 12\text{ cm}12 cm12, start text, space, c, m, end text by 20\text{ cm}20 cm20, start text, space, c, m, end text by 5\text{ cm}5 cm5, start text, space, c, m, end text. The only thing in the art box is a new pink eraser with the dimensions shown below.
Answer:
1196 cm3
Step-by-step explanation:
Answer:
1196
Step-by-step explanation:
Bryan is a waiter. He waits on a table of 4 whose bill comes to $110.31. If Bryan receives a 15% tip, approximately how much will he receive?
If Bryan receives a 15% tip, then he will receive an amount of approximately $16.55 as a tip.
In order to calculate the tip-amount, we need to multiply the total-bill by the tip percentage. In this case, the "bill-amount" is $110.31, and the tip percentage is 15%.
To find the tip amount, we can use the formula:
Tip amount = (Total bill) × (Tip percentage),
Simplifying further,
We get,
Tip amount = $110.31 × 0.15,
= $16.5465 (rounded to the nearest cent)
Therefore, Bryan will receive approximately $16.55 as a tip.
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If f(x) = 3x + 1 and g(x) = x − 3, find the quantity f divided by g of 8.
A. 125
B. 25
C. 20
D. 5
The quantity f divided by g of 8 is 5, which is answer choice D.
To find f divided by g of 8, we need to plug in x = 8 into both f(x) and g(x), then divide f(8) by g(8).
f(x) = 3x + 1
f(8) = 3(8) + 1
f(8) = 25
g(x) = x - 3
g(8) = 8 - 3
g(8) = 5
Now, we can divide f(8) by g(8) to get:
f(8) / g(8) = 25 / 5
f(8) / g(8) = 5
Alternatively, we can find f divided by g of x generally by first applying the functions to x:
f(x) / g(x) = (3x + 1) / (x - 3)
We can then plug in x = 8 and simplify:
f(8) g(8) = (3(8) + 1) / (8 - 3)
f(8) / g(8) = 25 / 5
f(8) / g(8) = 5
Regardless of the method we use, we find that f divided by g of 8 is 5.(option-d)
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the starting salaries of college instructors have a sd of $ 2000. how large a sample is needed if we wish to be 96% confident that our mean will be within $500 of the true mean salary of college instructors? round your answer to the next whole number.
Given:Standard deviation, s = $2000Confidence level = 96%Margin of error, E = $500We have to find the sample size, n.
Sample size formula is given as:\[n={\left(\frac{z\text{/}2\times s} {E}\right)}^{2}\]Where, z/2 is the z-score at a 96% confidence level. Using the standard normal table, we can get the value of z/2 as follows:z/2 = 1.750Incorporating all the values in the formula, we get:\[n={\left(\frac{1.750\times 2000}{500}\right)}^{2}\] Simplifying,\[n=21\]Therefore, a sample size of 21 is required if we wish to be 96% confident that our mean will be within $500 of the true mean salary of college instructors.
To determine the sample size needed to be 96% confident that the mean salary will be within $500 of the true mean salary, we can use the formula for sample size in a confidence interval.
The formula is:
n = (Z * σ / E)^2
Where:
n is the required sample size
Z is the z-score corresponding to the desired confidence level (in this case, 96% confidence level)
σ is the standard deviation of the population (given as $2000)
E is the maximum error tolerance (given as $500)
First, we need to find the z-score corresponding to a 96% confidence level. The remaining 4% is split evenly between the two tails of the distribution, so we look up the z-score that corresponds to the upper tail of 2% (100% - 96% = 4% divided by 2).
Using a standard normal distribution table or a calculator, the z-score for a 2% upper tail is approximately 2.05.
Now we can substitute the values into the formula:
n = (Z * σ / E)^2
n = (2.05 * 2000 / 500)^2
Calculating this expression:
n = (4100 / 500)^2
n = 8.2^2
n = 67.24
Rounding up to the next whole number, the required sample size is approximately 68.
Therefore, a sample size of 68 is needed to be 96% confident that the mean salary will be within $500 of the true mean salary of college instructors.
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Given information: The starting salaries of college instructors have a standard deviation (SD) of $2000. The sample size that is needed if we want to be 96% confident that our mean will be within $500 of the true mean salary of college instructors is to be calculated.
Hence, 49 is the sample size that is needed if we want to be 96% confident that our mean will be within $500 of the true mean salary of college instructors.
The formula for the sample size required is as follows:
[tex]n = [(Z \times \sigma) / E]^{2}[/tex]
Here, Z is the value from the normal distribution for a given confidence level, σ is population standard deviation, E is the maximum error or the margin of error, which is [tex]\$500n = [(Z \times \sigma) / E]^2[/tex]
On substituting the given values, we get:
[tex]n = [(Z \times \sigma) / E]^2[/tex]
[tex]n= [(Z \times \$2000) / \$500]^2[/tex]
[tex]n = [(1.7507 \times \$2000) / \$500]^2[/tex]
[tex]n = (7.003 \times 7.003)[/tex]
n = 49 (rounded off to the next whole number)
Hence, 49 is the sample size that is needed if we want to be 96% confident that our mean will be within $500 of the true mean salary of college instructors.
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5/7+1/2+3/4
i need help please
Answer:
1.96428571429
Step-by-step explanation:
Answer:
55/28
Step-by-step explanation:
5×2+7/14+3/4
17/14+3/4
68+42/56
110/56
55/28
There are about 23 Hershey kisses in an 11-ounce bag of candy. Write and solve a proportion
that you can use to find the number of Hershey kisses in a 5-ounce bag.
Answer:
about 10 hershy kisses
Step-by-step explanation:
Sorry If wrong :(
Nike reported total revenues of $44.5 billion for the year ending in May 31, 2021. What percentage of this amount relates to sales of footwear? (Enter your answer as a percentage without the % symbol, e.g., if your answer is 35%, enter 35) 2.How much cash did Nike collect from customers in the year ending May 31, 2021? The balance sheet shows that accounts receivable increased by $1,714 during the year, but some of that amount relates to mergers and acquisitions rather than additional credit sales. You will get the right amount of increased receivables from additional credit sales during the year by looking at the operating section of the statement of cash flows. (Enter your answer in $ millions)
Nike reported total revenues of $44.5 billion for the year ending in May 31, 2021. Footwear accounted for 66% of Nike's total revenues in 2021, the percentage of Nike's total revenues that relates to sales of footwear is 66%.
How to explain the informationThe balance sheet shows that accounts receivable increased by $1,714 during the year, but some of that amount relates to mergers and acquisitions rather than additional credit sales. You will get the right amount of increased receivables from additional credit sales during the year by looking at the operating section of the statement of cash flows.
The operating section of the statement of cash flows shows that Nike collected $42.8 billion from customers in the year ending May 31, 2021. This is the amount of cash that Nike received from customers for the sales of its products and services.
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this is the question I meant to send
Answer:
30%
Step-by-step explanation:
A placement exam has a measure of x=500 and a standard deviation of s=100. If a student obtained the standard value z= 1.8, then the exam grade is: a. 400 b. 640 c.320 d.680
deviation of the children's ages is: a. 1.27 b. 1.62 c. 2:25 a.m. 1.97 dad Frecuencia xf Jeg gon.no 7 12 10 8 5 42 84 80 72 50 252 588 640 648 500
If a student obtained the standard value z= 1.8, then the exam grade is 680.
Given, a placement exam has a measure of x = 500 and a standard deviation of s = 100, and a student obtained the standard value z = 1.8, and we are to find the exam grade.
In order to find the exam grade, we can use the formula, z = (x - μ) / σ where x is the score, μ is the mean, and σ is the standard deviation.
Substituting the given values, we get1.8 = (x - 500) / 100
Multiplying both sides by 100, we get180 = x - 500
Adding 500 to both sides, we get680 = x
Therefore, the exam grade is 680.So, the correct option is d. 680.
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Carly loves to run while Riley prefers walking. Carly can run 3 miles per hour faster
than her sister Riley can walk the same distance. If Carly ran 15 miles in the same time
it took Riley to walk 9 miles, which equation can be used to find the speed of each
sister?
Answer:
Step-by-step explanation:
help pls first awnser get brainest
Answer:
124
Step-by-step explanation:
the top square is 16 by 6 which will give you an area of 124 the bottom square has dimensions of 2 by 14 which is 28 add those numbers together to get your answer.
El elemento neutro de la suma es el 1.
Can someone help me with this. Will Mark brainliest.
Answer:
pt B: (-1, -8)
Step-by-step explanation:
(x - 7)/2 = -4
x - 7 = -8
x = -1
(y-6)/2 = -7
y - 6 = -14
y = -8
Some unsound arguments are valid. True or False?
The statement "Some unsound arguments are valid" is false.
The statement "Some unsound arguments are valid" is false.
A valid argument is a statement that follows the rules of logic.
An argument is known to be sound when it is valid and has true premises. When the premises of an argument are correct, the argument is considered sound. When an argument is valid, it follows logically from its premises, which are the statements that provide evidence or support for the argument's conclusion.
The unsound argument is the one that contains at least one false premise.
The sound argument is the one that contains only true premises and is valid (that is, follows logically from the premises).
If an argument is unsound, it can never be valid because it contains at least one false premise.
Therefore, the statement "Some unsound arguments are valid" is false.
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Use the Laplace transform to solve the following initial value problems. 2 a) ' +5/- y = 0, (O) = -1/(0) = 3 b) +4+ 30) = -1. V(0) - 2
To solve the initial value problems using the Laplace transform, we can apply the Laplace transform to the given differential equations and initial conditions.
For the first problem, the Laplace transform of the differential equation is s^2Y(s) + 5sY(s) + 2Y(s) = 0. Solving for Y(s), we find Y(s) = -3/(s+1).
Taking the inverse Laplace transform, we obtain the solution y(t) = -3e^(-t). For the second problem, the Laplace transform of the differential equation is sY(s) + 4Y(s) + 3/(s+1) = -2. Solving for Y(s), we find Y(s) = (-2s - 1)/(s^2 + 4s + 3). Taking the inverse Laplace transform, we obtain the solution y(t) = (-2t - 1)e^(-t).
a) The Laplace transform of the given differential equation is:
s^2Y(s) + 5sY(s) + 2Y(s) = 0
Using the initial condition Y(0) = -1 and Y'(0) = 3, we can apply the initial value theorem to obtain:
Y(s) = -1/s + 3
Taking the inverse Laplace transform of Y(s), we find:
y(t) = -3e^(-t)
b) The Laplace transform of the given differential equation is:
sY(s) + 4Y(s) + 3/(s+1) = -2
Using the initial condition Y(0) = -1, we can apply the initial value theorem to obtain:
Y(s) = (-2s - 1)/(s^2 + 4s + 3)
Taking the inverse Laplace transform of Y(s), we find:
y(t) = (-2t - 1)e^(-t)
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what are the zeros of the quadratic function? f(x)=2x2+x-3
Answer: The zeros of the quadratic function are: 5/2+(1/2)*sqrt(31), 5/2-(1/2)*sqrt(31)
Step-by-step explanation:
solve for x. help please
Answer:
x=6
Step-by-step explanation:
[tex]\frac{9}{3} =\frac{6}{2}[/tex]
please please please help
Answer:
I wanna say 16 but im not sure
Step-by-step explanation:
HELP PLEASE I WILL GIVE THE BRAINLIEST ANSWER Parking meter that is 1.6 m tall cast a shadow 3.6 m long at the same time a tree cast a shadow 9 m long
Answer:
I am not able to answer your question because I am unsure of what to solve for. :/
Step-by-step explanation:
What is the value of y when x=-1?
P
Answer:
is there an equation to find y? Because all you gave was x=-1
Who is Pythagorean? when was he born? when did he die?
Answer:
" Pythagoras established the first Pythagorean community in Crotone, Italy. Early Pythagorean communities spread throughout Magna Graecia. "
"was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism . " <---------- Credits to: Yahoo
He was born in about 570 BC on the Greek island of Samos
He died in 495 BC
Student grades on a recent science test follow; 78, 81, 89, 75, 76, 91, 10963,
80, 87, 91, 95. Find the MEAN (average) to the nearest tenth.
• 76.9
• 83.0
• 83.8
• 83.3
Answer:
b
Step-by-step explanation:
took the test good luck
Answer:
Explained below
Step-by-step explanation:
I shall explain this
Add all the numbers together and divide by the number of numbers
[tex]78 + 81 + 89 + 75 + 76 + 91 + 10963 + 80 + 87 + 91 + 95 = answer \div 11 [/tex]