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Solve the given system - or show that no solution exists: \[ \begin{aligned} x+2 y &=& 1 \\ 3 x+2 y+& 4 z=& 7 \\ -2 x+y-& 2 z=&-1 \end{aligned} \]
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Consider the system of equations \[ \begin{aligned} &x+y-z=a \\ &x-y+2 z=b . \end{aligned} \]
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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} \ a) Find the general solution of the homogeneous ...
by MathsGee Platinum
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asked in Mathematics 1 hour ago
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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?
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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 ...
by MathsGee Platinum
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asked in Mathematics 1 hour ago
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Show that the matrix \(\lim _{k \rightarrow \infty} T^{k}\) has all of its columns equal to \(P_{\infty}\).
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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 ...
by MathsGee Platinum
(104,456 points)
asked in Mathematics 1 hour ago
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A certain plant species has either red (dominant), pink (hybred), or white (recesive) flowers, depending on its genotype.
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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. If you cross a pink plant wi ...
by MathsGee Platinum
(104,456 points)
asked in Mathematics 1 hour ago
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Multinational companies in the Americas, Asia, and Europe have assets of \(\$ 4\) trillion.
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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. At the start, \(\$ 2\) trillion are in the Americas and \( ...
by MathsGee Platinum
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asked in Mathematics 1 hour ago
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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
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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
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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 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 ...
by MathsGee Platinum
(104,456 points)
asked in Mathematics 2 hours ago
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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:
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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?
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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?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 ...
by MathsGee Platinum
(104,456 points)
asked in Mathematics 2 hours ago
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[Monty Hall Problem] Suppose you're on a game show, and you're given the choice of three doors:
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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: Behind one door is a car; behind the others, goats. Yo ...
by MathsGee Platinum
(104,456 points)
asked in Mathematics 2 hours ago
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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?

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