How to check if something is an eigenvalue of a matrix?

Answers

Answer 1
If the square matrix is [A], then any eigenvalue, λ, satisfied the equation
[A] = λ[I]
where [I] is the identity matrix of the same size as [A].

To test whether λ is an eigenvalue, verify that
det([A] - λ[I]) = 0

Example:
Test whether 25.06 is an eigenvalue of the following matrix:
[tex][A]= \left[\begin{array}{ccc}15&0&-1\\0&25&1\\-1&1&9\end{array}\right] [/tex]
Test the determinant of [A] - 25.06[I] to see whether it is zero.
[tex]det( \left[\begin{array}{ccc}15&0&-1\\0&25&1\\-1&1&9\end{array}\right] \, - 25.06 \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] ) \\ =det \left[\begin{array}{ccc}-10.06&0&-1\\0&-0.06&1\\-1&1&-16.06\end{array}\right] \\ = 0.4262[/tex]

This determinant is not zero, but it is small compared with the diagonal elements of [A].
In practical terms (such as in engineering or physics) it is close to an eigenvalue of [A].
The actual eigenvalue is 25.0626


Related Questions

Write the equation of the line in standard form when the slope is -7 and the line goes through

(-2, 5). Graph the line.

Answers

The best fit for this equation would be a point slope form, which is (y-y)=m(x-x), where m is the slope and the second y and x variables are a point. 
So all we need to do is input them in!
(y-5)=-7(x+2)
Some explanations here:
Why is the 5 and 2 in those places? Why aren't they backwards? 
That is because the x number should always go with the x variable and the same with y. 
Why is 2 positive?
It is very hard to explain, but the number becomes a positive when the number is negative. It's just how it works. Ask Einstein.

Convert 45 miles per hour to feet per hour. Round your answer to the nearest hundredth, if necessary.

Answers

1 mile = 5280 feet

45 x 5280 = 237,600 feet per hour

9 divided by 3/2?????????????

Answers

9 divided by 3/2
= 9 (2/3)
= 6

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

There were 5 people who bought tickets to a football game. They bought 3 tickets each. How many tickets were bought in all?

Answers

5 people times 3 tickets each
5 times 3 = 15

15 tickets in all
So basically you want to say,

five people who each bought 3 tickets

Or, 

five groups of 3 tickets.

So five groups of 3 tickets would be,

3 + 3 + 3 + 3 + 3,

or 3 * 5.

3 * 5 = 15.

branliest offered 10 points for each question

least to greatest
square root of 8, -2/5, -1, 0.6, square root of 6


-8,3, negative square root of 5, 2.6, -1.5, square root of 5

-8.3,negagitive square root of 80, -17/2, -8.25, negative square root of 100

Answers

1. -2/5, 0.6, squ rt of 6, squ rt of 8
2. -8.3, negative squ rt of 5, -1.5, squ rt of 5, 2.6
3. neg. squ rt of 100, -17/2, neg. squ rt of 80, -8.3, -8.25

HOPE IT HELPED 

whats the simple answer and way to solve -46+ x=25

Answers

x=71

-46+x=25
add 46 to both sides (you do the inverse!)
x=71
Add -46 to 25. Which would be 71. So x=71

what is the value of the expression? (11 - 4) * (6 + 5) A.18 B.47 C.77 D.117

Answers

According to the order of operations, evaluate operations within parentheses first.
11-4=7
6+5=11

Rewrite the expression
7*11

Evaluate
77

Final answer: C

Which expression is equivalent to −1.3+(−4.9)+(−2.6) ?

a −(1.3−4.9)+(−2.6)
b −1.3+(4.9+2.6)
c (1.3+4.9+2.6)
d −1.3−(4.9+2.6)

Answers

The answer for this question would be D) -1.3 - (4.9 + 2.6) or the fourth option because the solution for this equation is the same as -1.3 + (-4.9) + (-2.6) which both = -8.8. So since they both have the same result, both expressions are equivalent.
Final answer:

The equivalent expression to -1.3+(-4.9)+(-2.6) is -1.3 - 4.9 - 2.6, which is represented by option d, -1.3 - (4.9 + 2.6).

Explanation:

The subject of this question is a mathematical calculation, more specifically adding negative numbers.

To answer the student's question about which expression is equivalent to -1.3+(-4.9)+(-2.6), we first need to understand that adding a negative number is the same as subtraction. Therefore, the expression can be written as -1.3 - 4.9 - 2.6.

If we look at the options:

Option a, −(1.3−4.9)+(−2.6) is not correct because subtracting a negative number should be the same as adding; Option b, −1.3+(4.9+2.6) is incorrect as well; Option c, (1.3+4.9+2.6) is not equivalent because the signs of all numbers are positive; Option d, −1.3−(4.9+2.6) is indeed the correct option, because it represents the operation of subtraction as originally described.

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Please help me :/ If AB=BC, then DE=2(AB). AB=6 and BC=6. What can you conclude

Answers

Final Answer:

Given AB = BC = 6, and DE = 2(AB), then DE = 2 * 6 = 12. Therefore, DE equals 12 units.

Explanation:

In the problem, it's stated that AB = BC = 6 units. This means that both AB and BC are equal in length, each measuring 6 units. As per the given relationship, DE is twice the length of AB. Substituting the known value of AB as 6 units into the expression for DE, we get DE = 2 * 6 = 12 units.

The equality of AB and BC implies that the triangle ABC is an isosceles triangle, where AB and BC are the congruent sides. Consequently, the line segment DE, which is related to AB, shares the same length as BC, making DE also equal to 6 units. However, as per the given relationship DE = 2 * AB, DE is calculated as 2 times the length of AB. Substituting AB = 6 units into the equation, DE = 2 * 6 = 12 units.

Therefore, following the given relationship between DE and AB and using the fact that AB = BC, we can confidently conclude that the length of DE is 12 units. This is determined by doubling the known length of AB, which is established by the equality of AB and BC in the context of an isosceles triangle.

The second side of a triangular deck is 3 feet longer than the shortest side and a third side that is 3 feet shorter than twice the length of the shortest side. if the perimeter of the deck is 68 feet, what are the lengths of the three sides?

Answers

The perimeter of a triangle is:

P = a + b + c

 

We are given that:

b = a + 3

c = 2 a – 3

 

Therefore:

68 = a + a + 3 + 2 a – 3

68 = 4 a

a = 17

 

and,

b = a + 3 = 20

c = 2a – 3 = 31

The shortest side of the triangle measures 17 feet.

The second side of the triangle measures 20 feet.

The third side of the triangle measures 31 feet.

What is the length of the three sides?

The perimeter of a triangle is the sum of the length of the three sides of the triangle.

Let the shortest side be represented with s.

The second side = 3 + s

The third side = 2s - 3

2s - 3 + 3 + s + s = 68

4s = 68

s = 17

The second side = 17 + 3 = 20

The third side = = (2 x 17) - 3 = 31

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Noel Devine bought a new dishwasher for $320. He paid $20 down and made 10 monthly payments of $34. What actual yearly interest rate did Noel pay?
    
  A. 14.55%
  B. 29.09%
  C. 34.38%
  D. 68.75%

Answers

The yearly interest rate that Noel payed is 29.09%

Solution:

Cost price of Dishwasher bought by Noel Divine = $ 320

Down payment = $ 20

Amount given in one installment= $ 34

Total Amount paid in 10 Installment = $34 ×10=$ 340

Total amount paid for Dishwasher by Noel Divine = $340 + $ 20 = $ 360

Interest paid by noel = $ 360 - $ 320= $ 40

As the interest will be simple interest

Simple interest =[tex]\frac{Principal \times \text{time} \ \text{rate}}{100}[/tex]

40=[tex]\frac{320 \times R \times \frac{10}{12}}{100}[/tex]

R= [tex]\frac{48000}{3200}[/tex]=15% →→Option A



Write an equation for the vertical translation. y=1/2x; 18 units down

Answers

Final answer:

To write an equation for a vertical translation, subtract the amount of the translation from the original equation. In this case, the equation y = 1/2x becomes y = 1/2x - 18, representing a vertical translation of 18 units downwards.

Explanation:

To write an equation for the vertical translation, we start with the equation y = 1/2x. Since we need to shift the graph 18 units down, the equation becomes y = 1/2x - 18. This equation represents a vertical translation of 18 units downwards.

If the value of x decreases by 6, how does the value of m(x + 9) change?

Answers

Since the value of x changes, it changes the answer to the equation.
Your answer is:
decreases by 6cm

Is 4x + the square root of y = 12 a linear function

Answers

I wouldn't say so, as if you rearrange that equation you get sqr root y = 12 - 4x. Then you square everything to get the value of y so you would end up with 144 - 16x^2.
Therefore, the x value has a power, so it would be a curved line
Final answer:

The equation 4x + √y = 12 is a non-linear function because of the square root term. Non-linear functions do not have a constant rate of change and their graphs are not straight lines.

Explanation:

The equation 4x + √y = 12 is not a linear function. A linear function is defined as a function that can be represented by a straight line. However, this equation contains a square root term, which makes it a non-linear function. To determine the type of function, it is important to consider the rules and properties of different function types.

In this case, the equation represents a non-linear function because of the square root term. Non-linear functions do not have a constant rate of change and their graphs are not straight lines. The square root term introduces a curve in the graph.

For example, let's say y = 4, then we can solve for x: 4x + √y = 12, which simplifies to 4x + 2 = 12. Solving for x, we get x = 2. So, for y = 4, x = 2. If we continue to substitute different values for y, we will see that the relationship between x and y is not linear.

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Volume is a three-dimensional measure.
true
false

Answers

True, volume is a tree dimensional measure.

8x-34=5x+2. What is x?

Answers

8x - 5x = 34 + 2

3x = 36

3x/3 = 36/3

x = 12

hope this helps
If we're solving for x, that would equal x = 12.

I hope this helps! :>

To change from one unit to another in the metric system, multiply or divide by multiples of (answer).

Answers

You can change from one unit to another in the metric system by multiplying or dividing by multiples of 10. For example, to convert centimeters into decimeters, you divide the number of centimeters by 10. To convert meters into decimeters, you multiply the number of meters by 10. One advantage of the metric system is that conversion between units is easier than in systems of measurement that require memorizing more complicated conversions.

Answer:

To change from one unit to another in the metric system, multiply or divide by multiples of 10.

Step-by-step explanation:

2.
The range of the following relation: R: {(3, -2), (1, 2), (-1, -4), (-1, 2)} is (1 point)

a) {-1, 1, 3}

b) {-1, -1, 1, 3}

c) {-4, -2, 2, 2}

d) {-4, -2, 2}

Answers

Its d  
The 2 is not repeated in the set.

Answer:

D.

Step-by-step explanation:

The range is the (y) value. And you never repeat a number when finding the relation or domain (x).  Therefor the best answer would be D.

Its not A because the numbers are for the domain (X value; First column)

Not B because its also for the Domain and it repeats -1 twice

Not C because it repeats 2 twice

Making D the reasonable answer

I hope this helps :))

In an orchard, for every 5 green apples there are 2 red apples. What is the ratio of green apples to red apples?

Answers

The ratio would be 5:2

how to factor x^4+x^2-20

Answers

(x2 + 5) • (x + 2) • (x - 2) Here's the anwser

Aliza needs to run at a rate faster than 8.8 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below:

He concludes that she is not running fast enough to exceed her fastest time. 

Answers

Answer:

Check: He used an incorrect time ratio converting hours to minutes

Check: He incorrectly concluded that she is not running fast enough

Do not check: His units do not cancel

Do not check: He used an incorrect distance ratio converting miles to feet

Do not check: He cannot determine her average rate in miles per hour after only 15 minutes

Step-by-step explanation:

You're welcome bud :)

15 pts!! Find an equation of the line that satisfies the given conditions: through (2,4) & parallel to the x axis.

Answers

If the c axus is 2 then you go right by two (simple) then with your y axus you go up four (simple) thrn you subtract backwards until your dots are lined up
If it is parallel, It has no slope. So:

y = mx + b
y = 0x + b

Now lets plug in our point:

y = 0x + b
4 = 0(2) + b
4 = b

So;

y = 0x + 4
y = 4

Hope this helps!

Simplify 81.56 + n - 2.55.
A)79.10 - n
B)79.01 + n
C)81.56 - 2.55n

Answers

The answer is B)79.01 + n

The correct answer would be 
B) 79.01 + n
I hope this helps! :)

what is -1/3+5(negative one over three plus 5) please help me im confused

Answers

I believe the correct answer to that would be 4 2/3

    Math Natalia Gonzalez You already owed your friend $6. This morning you borrowed $4 more and this afternoon you paid back $8. How much money do you owe your friend?

Answers

You owe your friend 2 dollars

Hi!!

The answer is 2!

Fun fact,my name is Natalia Gonzalez too!!

But

6+4=10

10-8= 2

Hope this helps ya

You are going running. For every mile you run, you burn 100 calories. In the equation below, m represents the number of miles you run, and c represents the number of calories you burn. The relationship between these two variables can be expressed by the following equation: c=100m, equals, 100, m Identify the dependent and independent variables.

Answers

The number of miles you run is Independent and the calories you burn is Dependent

Answer:

C is the dependent variable  

m is the independent variable

Step-by-step explanation:

 For every mile you run, you burn 100 calories. In the equation below, m represents the number of miles you run, and c represents the number of calories you burn

C= 100m

Number of calories burn depends on the number of miles you run

So calories C depends on the miles 'm'

C is the dependent variable because it depends on the value of 'm'

m is the independent variable

(8 - 4)x + 6 which property is being used?

Answers

Distributive property is being used to get 8x-4x+6.

Which expression can be used to find the slope of a line containing points (-3,2) and ( 7,-1)

Answers

-1-2=-3
7+3=10

slope is -3/10

y-2= -3/10(x+3)

y-2=(-3/10)x-9/10

y-2=(-3/10)x - 9/10

y=(-3/10)x+ 11/10

Doug is going to the store to stock up on food for his dog. While in the store, Doug decides to buy a single bag of dog treats as well. If a large bag of dog food costs $57 and a bag of dog treats costs $9, how many large bags of dog food, x, did Doug buy if he spent $180 and all prices already include sales tax?

Answers

WELL if he only bought a single bag of treats we just need to subtract $9 from his total amount spent, then we can just worry about how many bags of dog food he bought.

180 - 9 = 171

If each bag of dog food costs $57 then we just divide it with the remaining total.

171 / 57 = 3


WHICH MEEEAANNNS:

Doug bought 3 bags of dog food. c:

Final answer:

To find the number of large bags of dog food Doug bought, use the given prices and total spent in the store.

Explanation:

Doug bought 3 large bags of dog food.

To solve this problem, we can set up the equation: $57x + $9 = $180. From here, we can find x by rearranging the equation to solve for x.

Therefore, Doug bought 3 large bags of dog food, as each large bag costs $57 and he spent $180 in total.

0.008 is 1 tenth of what decimal

Answers

0.08, Hope it helped
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