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Say you have $k$ linear algebraic equations in $n$ variables; in matrix form we write $A X=Y$. Give a proof or counterexample for each of the following.
Say you have $k$ linear algebraic equations in $n$ variables; in matrix form we write $A X=Y$. Give a proof or counterexample for each of the following.Say you have $k$ linear algebraic equations in $n$ variables; in matrix form we write $A X=Y$. Give a proof or counterexample for each of the fo ...
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Solve the given system - or show that no solution exists: \begin{aligned} x+2 y &=& 1 \\ 3 x+2 y+& 4 z=& 7 \\ -2 x+y-& 2 z=&-1 \end{aligned}
Solve the given system - or show that no solution exists: \begin{aligned} x+2 y &=& 1 \\ 3 x+2 y+& 4 z=& 7 \\ -2 x+y-& 2 z=&-1 \end{aligned}Solve the given system - or show that no solution exists: \ \begin{aligned} x+2 y &amp;=&amp; 1 \\ 3 x+2 y+&amp; 4 z=&amp; 7 \\ -2 x+y-&amp; 2 z=&amp ...
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Consider the system of equations \begin{aligned} &x+y-z=a \\ &x-y+2 z=b . \end{aligned}
Consider the system of equations \begin{aligned} &x+y-z=a \\ &x-y+2 z=b . \end{aligned}Consider the system of equations \ \begin{aligned} &amp;x+y-z=a \\ &amp;x-y+2 z=b . \end{aligned} \ a) Find the general solution of the homogeneous ...
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If $A$ is a $5 \times 5$ matrix with $\operatorname{det} A=-1$, compute $\operatorname{det}(-2 A)$.
If $A$ is a $5 \times 5$ matrix with $\operatorname{det} A=-1$, compute $\operatorname{det}(-2 A)$.If $A$ is a $5 \times 5$ matrix with $\operatorname{det} A=-1$, compute $\operatorname{det}(-2 A)$. ...
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What was the initial distribution of the milk?
What was the initial distribution of the milk?Snow White distributed 21 liters of milk among the seven dwarfs. The first dwarf then distributed the contents of his pail evenly to the pails of othe ...
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Let $T$ be the transition matrix for a Markov chain. If there is some power $k$ for which all of the elements of $T^{k}$ are positive, show that all the elements of $T^{k+1}$ are positive.Let $T$ be the transition matrix for a Markov chain. If there is some power $k$ for which all of the elements of $T^{k}$ are positive, show that ...
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Show that the matrix $\lim _{k \rightarrow \infty} T^{k}$ has all of its columns equal to $P_{\infty}$.
Show that the matrix $\lim _{k \rightarrow \infty} T^{k}$ has all of its columns equal to $P_{\infty}$.If $T$ is the transition matrix of a regular Markov process (so for some $k$ all the entries of $T^{k}$ are positive), we know there is a probab ...
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Form a Markov chain by following the job of a randomly chosen child of a given family through several generations. Set up the matrix of transition probabilities.
Form a Markov chain by following the job of a randomly chosen child of a given family through several generations. Set up the matrix of transition probabilities.Assume (naively) that a person's job can be classified as professional, skilled, or unskilled. Assume that, of the children of professional parents, 8 ...
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A certain plant species has either red (dominant), pink (hybred), or white (recesive) flowers, depending on its genotype.
A certain plant species has either red (dominant), pink (hybred), or white (recesive) flowers, depending on its genotype.A certain plant species has either red (dominant), pink (hybred), or white (recesive) flowers, depending on its genotype. If you cross a pink plant wi ...
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Multinational companies in the Americas, Asia, and Europe have assets of $\ 4$ trillion.
Multinational companies in the Americas, Asia, and Europe have assets of $\ 4$ trillion.Multinational companies in the Americas, Asia, and Europe have assets of $\ 4$ trillion. At the start, $\ 2$ trillion are in the Americas and $... close 0 answers 4 views Suppose there is an epidemic in which every month half of those who are well become sick, half of those who are sick get well, and a quarter of those who are sick die. Find the steady state for the corresponding Markov processSuppose there is an epidemic in which every month half of those who are well become sick, half of those who are sick get well, and a quarter of those ... close 0 answers 5 views A long queue in front of a Moscow market in the Stalin era sees the butcher whisper to the first in line. He tells her "Yes, there is steak today." She tells the one behind her and so on down the line.A long queue in front of a Moscow market in the Stalin era sees the butcher whisper to the first in line. He tells her &quot;Yes, there is steak today ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let \(T$ be the transition matrix of a Markov process. If $P$ is a probability vector, show that $T P$ is also a probability vector.
Let $T$ be the transition matrix of a Markov process. If $P$ is a probability vector, show that $T P$ is also a probability vector.Let $T$ be the transition matrix of a Markov process. If $P$ is a probability vector, show that $T P$ is also a probability vector. ...
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Say you pick a point $(x, y)$ at random in the unit square $0 \leq x \leq 1,0 \leq y \leq 1$. Compute the probability it will be in the set
Say you pick a point $(x, y)$ at random in the unit square $0 \leq x \leq 1,0 \leq y \leq 1$. Compute the probability it will be in the setSay you pick a point $(x, y)$ at random in the unit square $0 \leq x \leq 1,0 \leq y \leq 1$. Compute the probability it will be in the set \ S=\ ...
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Say you pick a point $x$ at random in the interval $0 \leq x \leq 1$. What is the probbility that it will be in the set
Say you pick a point $x$ at random in the interval $0 \leq x \leq 1$. What is the probbility that it will be in the setSay you pick a point $x$ at random in the interval $0 \leq x \leq 1$. What is the probability that it will be in the set a) $S=\{x \leq 1 / 2$ a ...
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A number, $k$, of people are subjected to a blood test, the result of which is either "positive" or "negative". It can be processed in two ways:
A number, $k$, of people are subjected to a blood test, the result of which is either "positive" or "negative". It can be processed in two ways:A number, $k$, of people are subjected to a blood test, the result of which is either &quot;positive&quot; or &quot;negative&quot;. It can be proces ...
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Would you accept a gamble that offers a 10-percent chance to win $\ 95$ and a 90-percent chance to lose \$5? 0 answers 5 views Would you accept a gamble that offers a 10-percent chance to win $\ 95$ and a 90-percent chance to lose \$5?a). Would you accept a gamble that offers a 10-percent chance to win $\ 95$ and a 90-percent chance to lose \\$5? b). Would you pay $\ 5$ to part ...
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In an oft-cited experiment the psychologists Kahneman and Tversky asked a group of subjects to imagine the outbreak of an unusual disease, expected to kill 600 people, and to choose between two public health programs to combat it.In an oft-cited experiment the psychologists Kahneman and Tversky asked a group of subjects to imagine the outbreak of an unusual disease, expected to ...
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[Monty Hall Problem] Suppose you're on a game show, and you're given the choice of three doors:
[Monty Hall Problem] Suppose you're on a game show, and you're given the choice of three doors:Monty Hall Problem Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. Yo ...
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The next three players in a game win $30 \%, 20 \%$ and $25 \%$ of the time, respectively. What is the likelihood that none of them will win this time?
The next three players in a game win $30 \%, 20 \%$ and $25 \%$ of the time, respectively. What is the likelihood that none of them will win this time?The next three players in a game win $30 \%, 20 \%$ and $25 \%$ of the time, respectively. What is the likelihood that none of them will win this ...