The matrix exponential e^At for the given system is computed using diagonalization of matrix A and the formula e^At = P * E * P^(-1), where P is the matrix of eigenvectors, E is the diagonal matrix of exponential eigenvalues, and P^(-1) is the inverse of P.
To compute the matrix exponential e^At for the given system x' = Ax, where A is the coefficient matrix, we can follow the steps outlined below:
Step 1: Diagonalize the matrix A.
Find the eigenvalues λi of matrix A by solving the characteristic equation |A - λI| = 0, where I is the identity matrix.Find the corresponding eigenvectors vi for each eigenvalue λi.Form the diagonal matrix D with the eigenvalues λi as diagonal elements.Form the matrix P with the eigenvectors vi as columns.Step 2: Compute the matrix exponential of D.
Take the exponential of each diagonal element of D to obtain the diagonal matrix E = e^D.Step 3: Compute the matrix exponential e^At.
Use the formula e^At = P * E * P^(-1), where P^(-1) is the inverse of matrix P.Now, let's apply these steps to the given system x'1 = 25x1 - 25x2 and x'2 = 20x1 - 20x2.Step 1: Diagonalize matrix A.
The coefficient matrix A is:| 25 -25 |
A = | |
| 20 -20 |
Computing the eigenvalues λi, we find λ1 = 0 and λ2 = 5.Corresponding eigenvectors vi are v1 = [1, 1] and v2 = [1, 4].Forming the diagonal matrix D:| 0 0 |
D = | |
| 0 5 |
Forming the matrix P:| 1 1 |
P = | |
| 1 4 |
Step 2: Compute the matrix exponential of D.
Taking the exponential of each diagonal element, we have E = e^D:| e^0 0 |
E = | |
| 0 e^5 |
Step 3: Compute the matrix exponential e^At.
Using the formula e^At = P * E * P^(-1), where P^(-1) is the inverse of matrix P:e^At = P * E * P^(-1)
Performing the matrix multiplication, we obtain the matrix exponential e^At.
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write the equation of the line in fully simplified slope-intercept form.
Step-by-step explanation:
świnka pepapomoże to zmieniam o tym zakładem ubezpieczeń i bankowości elektronicznej na tablecie i
The perimeter of a rectangle is 35cm. The length is 5cm. Write and
solve an equation to find the width of the rectangle.
Answer:
P = 2L + 2W
35 cm = 2(5 cm) + 2(W cm)
W = 12.5 cm
Step-by-step explanation:
P = 2L + 2W
35 cm = 2(5 cm) + 2(W cm)
35 cm - 10 cm = 2W cm
2W cm = 25 cm
w cm = 12.5 cm
Step-by-step explanation:
step 1. a rectangle has 2 sets of congruent sides; we will call them l and w.
step 2. P (perimeter) = l + l + w + w = 35
step 3. 35 = 5 + 5 + 2w
step 4. 25 = 2w
step 5. w(width) = 12.5 cm.
part of me wants to say that the answer is A , but the other part of me is saying the answer is D, which one is it?
Answer:
Pretty sure it's A
On a team, 4 girls and 2 boys scored a total of 28 points. The difference between the number of points scored by the 4 girls and the number of points scored by the 2 boys is 12. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each boy Each girl scored points.
Answer:
Each girl earned 2 points
Each boy earned 5 points
Step-by-step explanation:
Let x represent the number of points one girl earned
Let y represent the number of points one boy earned
4x + 2y = 28
4x - 2y = 12
8y = 40
y = 5 points
4x + (2)(5) = 28
4x + 20 = 28
4x = 8
x = 2 points
Each girl earned 2 points
Each boy earned 5 points
which function defines the sequence -16,-22,-28,-34 where f(10)= -70
Answer:
f(n) = -6n - 10.
Step-by-step explanation:
This is arithmetic sequence with first term a1 = -16 and common difference d = -6.
So f(n) = a1 + d(n - 1)
= -16 - 6(n - 1)
= -16 - 6n + 6
= -6n - 10.
Checking:
f(10) = -6(10) - 10 = -70.
The function that defines the sequence is f(n) = -6n - 10.
What is an Arithmetic Sequence ?A sequence of numbers which have a relation between them and the consecutive numbers increase or decrease by a fixed amount is called as an Arithmetic Sequence.
The sequence given is -16,-22,-28,-34
This is arithmetic sequence
first term a1 = -16
common difference d = -6.
The nth term of an arithmetic sequence is given by
f(n) = a1 + d(n - 1)
f(n) = -16 - 6(n - 1)
f(n)= -16 - 6n + 6
f(n)= -6n - 10.
To verify this
f(10) = -6(10) - 10 = -70.
Therefore , The nth term is given by f(n)= -6n - 10.
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What is the slope and the y-intercept of a line whose equation is y=-4x-7
A. slope = -4; y-intercept = 7
B. slope = 4; y-intercept = -7
C. slope = -4; y-intercept = -7
D. slope = -7; y-intercept = -4
compare the equation with the formula y=mx+c and you will get the value of slope and the y intercept.
For example - y= 3x +4
On comparing y=mx+c
We will get m= 3 and
y intercept = 4
ANSWER ASAP THEIRS A SCREEN SHOT TO HELP SHOW
AND TELL WHY PLEASE
what's
[tex]1024 \div 256[/tex]
Answer:
4 ...................
Step-by-step explanation:
hope the answer was helpful ......
Answer:
1024÷256=4
Step-by-step explanation:
hope u get that
50 POINTS!
In the diagram, d = 4. What is the value of x? Express your solution in simplest radical form, if necessary.
Answer:
146
Step-by-step explanation:
180=4+30+x
180=34+x
180-34=x
146=x
Please help me...???
Answer:
Step-by-step explanation:
77
Answer:
16.5 in³
Step-by-step explanation:
Length(L) = 2.2 in
breadth (b) = 1.5 in
height (h) = 5 in
Volume of the cuboid
= L * b * h
= 2.2 * 1.5 * 5
= 16.5 in³
Tony buys 2 boxes of chocolates. One is 4 in. 7 in. 8 in. And 8 in. 5 in. 6 in. Which box has the larger volume?
Answer:
Second box
Step-by-step explanation:
Volume (of the box) = length * width * height
Volume of first box is: 4 * 7 * 8 = 224
Volume of second box is: 8 * 5 * 6 = 240
Since 224 < 240, the volume of the second box has the larger value.
Answer:
second choice
Step-by-step explanation:
Find an ordered pair (x, y) that is a solution to the equation. x-3y = 6
Answer:
(0, -2)
(6, 0)
Step-by-step explanation:
pick a value for 'x', plug it into the equation, then solve for 'y'
pick a value for 'y', plug it into the equation, then solve for 'x'
Which of these statements is correct? Select all that apply.
A. A solution to the equation x
2 = 7 is x = √49
B. A solution to the equation x
2 = 15 is x = √15
C. A solution to the equation x
2 = 38 is x = ³√38
D. A solution to the equation x
3 = 3 is x = ³√27
Answer:
A and B lowkey don't feel like doing the rest cause I'm slow
Step-by-step explanation:
-75x + 200 represents a bank account balance after x months. What is the initial amount in the
account? What is the rate of change?
a x + b y is equal to 12
Answer:
y= -a*x + 12
b b
Step-by-step explanation:
ax+by=12 (subtract "ax" from both sides so that the one on the left will become zero and we will have "by" )
by= -ax+12(divide both side by "by" so that we will have the equation as "y=mx+b")
finally the result will be:
y= -a*x + 12
b b
The length of a recgangle is teice is width if the perimeter is 72 metre find the length and width of the rectangle
Answer:
Let width = b
Then length,l=2b
Perimeter =72
2(l+b)=72
2(2b+b)=72
2(3b)=72
6b=72
b=72/6=12
L=2b=12x2=24
Please hurry!!!!!!!!!!!!!!!!!!
Answer:
38
Step-by-step explanation:
Range is the largest number minus the smallest number
55-17=38
I hope I hurried enough
Answer:
Your question is not proper.Here, you said that range of data. But where is the data? How can you expect answer without giving proper question?
Plz help me step by step explanation would help for work plzzzz And Thank you PLEASE
Answer:
i hope this helps
Step-by-step explanation:
Answer:
r = -43. that's the result
pleasee helpp honestly im stuck i dont know how to graph this equation. it says to graph the funcion c(x)=3x-1
first take the 3 and place it over the negative one in quadrant 2
Answer:
apply number to the X when x= y = 3*0-1 =-1
x=1 y = 3*1-1 = 2
x = 2 y = 3*2-1 =5
n times 8.
The algebraic expression is _____.
Please help my assignment is due today
Answer:
Hope this helps, thank you !!
Can someone tell me the answer
Answer:
y=8x+4
Step-by-step explanation:
sasasaasasasasassasasasasasasasasasasasasasasa
Answer:
tatatatatatatatatatatatatata
Step-by-step explanation:
the duck is so cute
Answer:
DUCKYYY :DDD
Step-by-step explanation:
In the study of pesticide use and breast cancer, researchers evaluated pesticide use during the entire life of the respondents. How would you expect the results to have been affected if the researchers collected exposure history spanning the previous 20 years only?
Answer:
Kindly check explanation
Step-by-step explanation:
A common problem with most research designs is bias, which could be introduced win several ways one if which is the favored selection of certain variables rather than being randomized. In the scenario above, the sampling time frame introduces a bias into the design as the tune span of pesticide use does not allay with that of the exposure history of the respondent. Therefore an entire lifetime evaluation of one variable and just 20 years evaluation of the other introduces a sampling bias into the research design. Similarly, evaluation the type of pesticide usage over certain time period may need to be considered as the effect of very old pesticides may differ from those used very recently.
Help due tonight
Solve the following system of equations.
3x + y = -21
-3x - 3y = 15
X=
y =
Answer:
I have solved it in elimination method if you need it in another method let me know.
Step-by-step explanation:
3x+y=21
-x-y=5
2x=26
x=13
-3×13-3y=15
y= -18
HELP!!!!!!!!!!!!!!!!!!!!!!! :)
Hey there!
The answers are as follows:
7.)
m∠1 = 85
m∠2 = 95
m∠3 = 85
m∠4 = 85
8.)
m∠1 = 60
m∠2 = 120
m∠3 = 60
m∠4 = 120
9.)
they all equal 90
10.) No. Parallel lines do not cross each other, but these, if extended, would cross. You could use a protractor by measuring corresponding angles, and if they aren't equal, they aren't parallel.
Have a terrifcly amazing day!
Find The Area of the parallelogram...Explain.
Answer:
70Step-by-step explanation:
Recall that, in order to find the area of a parallelogram is to multiply height by base, and the height is 14, and the base is 5, so 14 x 5 = 70.
The cash register subtracts $4.00 from a $20 Coffee Cafe gift card for every medium coffee the customer buys. Use the graph to write an equation in slope-intercept form to represent this situation
I need help please!!
Answer:
Step-by-step explanation:
i think 90
What is the length of segment AC?
The y difference of the 2 lines are 6(you can just count these)
The x difference of the 2 lines are 8(again you can count this)
Now calculate distance using distance formula (the pythag theorem)
sqrt(6^2+8^2)=sqrt 100= 10
Therefore the distance of AC is 10.
What is the value of: (3.3) + (-1) - (-1.7)
Answer:
4
Step-by-step explanation:
3.3 + -1 is 2.3
2.3 - -1.7 is 4