How to find a matrix that transform a column matrix from linear to circular quantum mechanic?

Exercise 7.3.5 The following is a Markov (migration) matrix for three locations        1 5 1 5 2 5 2 5 2 5 1 5 2 5 2 5 2

fredd [130]

Answer:

Both get the same results that is,

$\left[\begin{array}{ccc}140\\160\\200\end{array}\right]$

Step-by-step explanation:

Given :

$\bf M=\left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]$

and initial population,

$\bf P=\left[\begin{array}{ccc}130\\300\\70\end{array}\right]$

a) - After two times, we will find in each position.

$P_2=[P].[M]^2=[P].[M].[M]$

$M^2=\left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]\times \left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]$

$=\frac{1}{25} \left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right]$

$\therefore\;\;\;\;\;\;\;\;\;\;\;P_2=\left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right] \times\left[\begin{array}{ccc}130\\300\\70\end{array}\right] = \left[\begin{array}{ccc}140\\160\\200\end{array}\right]$

b) - With in migration process, 500 people are numbered. There will be after a long time,

$After\;inifinite\;period=[M]^n.[P]$

$Then,\;we\;get\;the\;same\;result\;if\;we\;measure [M]^n=\frac{1}{25} \left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right]$

$=\left[\begin{array}{ccc}140\\160\\200\end{array}\right]$

4 0

3 years ago

The radius of the circle on a basketball court is 6 feet. What are the approximate circumstance and area of the circle?

Dimas [21]

Answer:

C= 38 in Approx

A=113 in^2 Aprprox

Step-by-step explanation:

Given data

radius= 6 ft

Circumference, C=2πr

substitute

C=2*3.142*6

C=37.704 in

Area A= πr^2

substitute

A=3.142*6^2

A=3.142*36

A=113.112 in^2

4 0

3 years ago

Please show work 7r + 21 = 49r

gulaghasi [49]

Answer:

1/2 = r

Step-by-step explanation:

7r + 21 = 49r

Subtract 7r from each side

7r-7r + 21 = 49r-7r

21 = 42r

Divide each side by 2

21/42 = 42r/42

1/2 = r

5 0

3 years ago

Read 2 more answers

The quadratic regression graphed on the coordinate grid represents the height of a road surface x meters from the center of the

andrew-mc [135]

The height of the surface increases, then decreases, from the center out to the sides of the road.

<h3>What is quadratic equation?</h3>

The polynomial having a degree of 2 is defined as the quadratic equation it means that the variable will have a maximum power of 2.

Let

y------> the height of the surface

x------> the road

we know that

The quadratic regression graphed represent a vertical parabola open downward

The function increase in the interval --------> (-5,0)

The function decrease in the interval --------> (0,5)

therefore

The height of the surface increases, then decreases, from the center out to the sides of the road.

To know more about quadratic equation follow

brainly.com/question/1214333

#SPJ1

5 0

2 years ago

Read 2 more answers

Gregorio took two tests. Find his z-score for each test. (Remember: The number of standard deviations between a score and the me

never [62]

I found the missing parts of this question.
Test A
Gregorio’s score 62 
Mean score 80 
Standard deviation 6 

Test B 
Gregorio's score 70 
Mean score 90 
Standard deviation 10 

a. Test A: 3; Test B: 2; Test A 
c. Test A: –2; Test B: –3; Test A 
b. Test A: –3; Test B: –2; Test B 
d. Test A: –3; Test B: –2; Test A


Refer to the attachment for the formula of z score:

test A: z = (62-80)/6 = -18/6 = -3
test B: z = (70-90)/10 = -20/10 = -2

B. Test A: –3; Test B: –2; Test B

5 0

3 years ago