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# Consider the regular transition matrix $A=\frac{1}{15}\left[\begin{array}{lllll} 4 & 2 & 5 & 1 & 3 \\ 1 & 3 & 4 & 5 & 2 \\ 3 &... ## Question ###### Consider the regular transition matrix \[ A=\frac{1}{15}\left[\begin{array}{lllll} 4 & 2 & 5 & 1 & 3 \\ 1 & 3 & 4 & 5 & 2 \\ 3 & 5 & 1 & 2 & 4 \\ 2 & 1 & 3 & 4 & 5 \\ 5 & 4 & 2 & 3 & 1 \end{array}\right]$ Note that the matrix $15 A$ contains each of the integers $1,2,3,4,$ and 5 once in every row and in every column. a. Using technology, compute a high power of $A$, such as $A^{20} .$ What do you observe? Make a co

Consider the regular transition matrix $A=\frac{1}{15}\left[\begin{array}{lllll} 4 & 2 & 5 & 1 & 3 \\ 1 & 3 & 4 & 5 & 2 \\ 3 & 5 & 1 & 2 & 4 \\ 2 & 1 & 3 & 4 & 5 \\ 5 & 4 & 2 & 3 & 1 \end{array}\right]$ Note that the matrix $15 A$ contains each of the integers $1,2,3,4,$ and 5 once in every row and in every column. a. Using technology, compute a high power of $A$, such as $A^{20} .$ What do you observe? Make a conjecture for $\lim _{t \rightarrow \infty} A^{t} .($ In part e, you will prove this conjecture.) b. Use technology to find the complex eigenvalues of A. Is matrix $A$ diagonalizable over $\mathbb{C} ?$ c. Find the equilibrium distribution $\vec{x}_{e q u}$ for $A,$ that is, the unique distribution vector in the eigenspace $E_{1}$ d. Without using Theorem 7.4 .1 (which was proven only for matrices that are diagonalizable over $\mathbb{R}$ ), show that $\lim _{t \rightarrow \infty}\left(A^{t} \vec{x}_{0}\right)=\vec{x}_{e q u}$ for any distribution vector $\vec{x}_{0} .$ Hint: Adapt the proof of Theorem 7.4 .1 to the complex case. e. Find $\lim _{t \rightarrow \infty} A^{t},$ proving your conjecture from part a. #### Similar Solved Questions

##### A series of laboratory experiments were carried out to investigate the relationship between the voltage level applied to an electronic component, and the lifetime weeks) ofthe component. particular; voltages the aet {5.6, 8,9,10} Vete considered and, each voltage. six components were tested until failure: Thus the total sample size was 36 components.We define the following: the lifetime of the component in weeks In( L) the natural logarithm of the lifetime. and the voliase level. Furthermore,
A series of laboratory experiments were carried out to investigate the relationship between the voltage level applied to an electronic component, and the lifetime weeks) ofthe component. particular; voltages the aet {5.6, 8,9,10} Vete considered and, each voltage. six components were tested until...
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##### A-haecullanLo In u ualiuie -ulli IL" FednEHF UWuhamlulLaRiumum Cae $rAlnetFCAetOhemlFu De 4n4ig Metet Taial Vny Die Hecab Fmeni nurfttem_ Dan IuAo"seIcly 'aluml sffennto Ir # e llussm Mhlnnentamzica icc Ibe Linal oh cury OL bull Jmul heb InuTdiale$ 6,Jufthus.Certc Fuqumlon imincuinely 2c: cullioTrchrkal cWrcy ofthc ball ondtab cnbInulirFrolectlesLSl Fevised IZINXHIZ
A-haec ullan Lo In u ualiuie -ulli IL" Fedn EH F U Wuhaml ulLaRiumum Cae $r AlnetFCAetOheml Fu De 4n4ig Metet Taial Vny Die Hecab Fmeni nurfttem_ Dan Iu Ao"seIcly 'aluml sffennto Ir # e llussm Mhlnn ent amzica icc Ibe Linal oh cury OL bull Jmul heb InuTdiale$ 6,Jufthus. Certc Fuqumlo...
##### The process by which carbohydrates are made available cells in the body begins with the movement of food from the mouth through the esophagus into the stomach and lastly into the small intestine when: the final steps for chemical digestion and absorption occur; Digestion the chemical mechanical breakdown of nutrienis. whenas absomption movement of nutrients in their simplest forn into the body - Absorption UWs primarily in the small intestine. Mechanical breakdown the physical breakdown of food
The process by which carbohydrates are made available cells in the body begins with the movement of food from the mouth through the esophagus into the stomach and lastly into the small intestine when: the final steps for chemical digestion and absorption occur; Digestion the chemical mechanical brea...
##### [6 % ] = V (s1d E)(q) [8 10 ] = v (sid c)(e) "sajn8y Inof Kpjeap? % anjeaua8a BulpuodsaJJo) a41 pue XV JO4334 a4 X JOJJaAU383 341 31EJ1pUJ 01 paau nof se souepd J1EU!pJOO) Kueu se asn Kileoujawoab aseald V Jo 5101284u861a pue sanjenuabia a41 puly (G)
[6 % ] = V (s1d E)(q) [8 10 ] = v (sid c)(e) "sajn8y Inof Kpjeap? % anjeaua8a BulpuodsaJJo) a41 pue XV JO4334 a4 X JOJJaAU383 341 31EJ1pUJ 01 paau nof se souepd J1EU!pJOO) Kueu se asn Kileoujawoab aseald V Jo 5101284u861a pue sanjenuabia a41 puly (G)...
##### SToichioMeTRY Solving for reactant using chemical equationWine goes bad soon after opening because the ethanol 'CH; CHzOH) in it reacts with oxygen 9as 0z from the air to form water (Hz0) and acetic acid (CH;COOH) the main ingredient of vinegar.What mass of acetic acid is produced by the reaction of 9.77 g of oxygen gas? Be sure your answer has the correct number of significant digits.Lxo
SToichioMeTRY Solving for reactant using chemical equation Wine goes bad soon after opening because the ethanol 'CH; CHzOH) in it reacts with oxygen 9as 0z from the air to form water (Hz0) and acetic acid (CH;COOH) the main ingredient of vinegar. What mass of acetic acid is produced by the rea...
##### The (lindrical and spherica/ coordinates of the point with rectangular coordinates (x,V,z) = (0,-Vz,z are (r,8,2) = (Vz,,42) and (0,0,0) = (2,1,1/3)(r,0,2)- (V2,n/4,42) and (p,0,p) = (4,1/4,7/3) (r,0,2) - (V2,1/2,42) and (p,0,0) = (2,0/2,11/4(r,0,2) - (V2,31/2.42) anc (p,0. p)=(2,31/2,01/4)
The (lindrical and spherica/ coordinates of the point with rectangular coordinates (x,V,z) = (0,-Vz,z are (r,8,2) = (Vz,,42) and (0,0,0) = (2,1,1/3) (r,0,2)- (V2,n/4,42) and (p,0,p) = (4,1/4,7/3) (r,0,2) - (V2,1/2,42) and (p,0,0) = (2,0/2,11/4 (r,0,2) - (V2,31/2.42) anc (p,0. p)=(2,31/2,01/4)...
##### Di Transcription factors are actual DNA sequences that control transcription.TrueFalseThe term q2 stands for the individuals who are Heterozygous in the population:TrueFalseRNAi (or RNA interference) describes how the splicesome creates alternative mRNAsTrue
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##### Increasing? intervals following which of the Onfor 0 21 ()by given derivative with w] only function 1 [0, 2.029] [1.077 , w] [2.029, Let f be the
increasing? intervals following which of the On for 0 2 1 () by given derivative with w] only function 1 [0, 2.029] [1.077 , w] [2.029, Let f be the...
##### 2x - [1(b) f(x) = X + Mx - 10lim f(x) = DNE [email protected] of horizontal asymptote: DNE
2x - [1 (b) f(x) = X + Mx - 10 lim f(x) = DNE [email protected] Equation of horizontal asymptote: DNE...
##### Critical values. Find the critkal value 20u ' Round critical value to two decimal placesHint: Note the difference between 2u0i and P 2Zoo1 is asking for the Z-score for the upper 1% of the curve It is the Z-score that separates that top 1% from the lowver 99% Ps in the previous question was asking for the Sth percentile. This would separate the upper 95% from the lowest 5%.
Critical values. Find the critkal value 20u ' Round critical value to two decimal places Hint: Note the difference between 2u0i and P 2Zoo1 is asking for the Z-score for the upper 1% of the curve It is the Z-score that separates that top 1% from the lowver 99% Ps in the previous question was as...
##### Transistor) Suppose that when Iransistor of" cerain type subjecled t0 an aceleraled life lest, the lifetime X (in weeks) has gamna distribution with mean 24 weeks and standard deviation |2 weeks What the probability that = trneisii will last between [2 and 24 weeks? What the probability that = transistor will Iast J most 24 Weeks" Is the median of the lifetime distribution less than 24" Why why nol?(Gemmu fuuetion): Repardling the EAm function, show that
Transistor) Suppose that when Iransistor of" cerain type subjecled t0 an aceleraled life lest, the lifetime X (in weeks) has gamna distribution with mean 24 weeks and standard deviation |2 weeks What the probability that = trneisii will last between [2 and 24 weeks? What the probability that = ...
##### Multiply both sides of each equation by the given number. See Section 2.1. $$-3 x+8 y-z=0 \quad \text { by }-3$$
Multiply both sides of each equation by the given number. See Section 2.1. $$-3 x+8 y-z=0 \quad \text { by }-3$$...
##### Question 4.1 (9 points) A random sample of 1000 Interviewees are asked whether they approve the job performance of & high -ranking executive The results suggest that approvals account for 70% and non-approvals account for 30 %_Calculate the Mean, and the standard deviation of this sample_ (2 points) Calculate the Standard Error of the Sample mean ' (i.e-, 69). (2 points) Calculate the upper and lower limlts of the confidence interval = of the support in the population (5 points) 9695 le
Question 4.1 (9 points) A random sample of 1000 Interviewees are asked whether they approve the job performance of & high -ranking executive The results suggest that approvals account for 70% and non-approvals account for 30 %_ Calculate the Mean, and the standard deviation of this sample_ (2 po...
##### A ray of light; P moving in air strikes a glass slab as shown below. N 01 02 Air 5o9 Refractive index = n1 = ]onGlass SlabRefractive index =n203RThe measure of angle 03 will beSelect one: Less than the measure of angle 01 b. More than the measure of angle 01 Equal to the measure of angle 01
A ray of light; P moving in air strikes a glass slab as shown below. N 01 02 Air 5o9 Refractive index = n1 = ] on Glass Slab Refractive index =n2 03 R The measure of angle 03 will be Select one: Less than the measure of angle 01 b. More than the measure of angle 01 Equal to the measure of angle 01...