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Mekhanik [1.2K]
3 years ago
14

Write the given linear system in matrix form. Assume X = x y z . dx dt = −3x + 6y − 9z dy dt = 7x − y dz dt = 10x + 6y + 3z

Mathematics
1 answer:
Yakvenalex [24]3 years ago
5 0

Answer:

Step-by-step explanation:

Consider the system:

\begin {Bmatrix}   \dfrac{dx}{dt}=-3x+6y-9z \\ \\ \dfrac{dy}{dt}=7x -y \\ \\ \dfrac{dz}{dt}= 10 x  + 6y + 3z\end {Bmatrix}

The matrix form of the system is:

\begin {bmatrix}   \dfrac{dx}{dt} \\ \\ \dfrac{dy}{dt} \\ \\ \dfrac{dz}{dt}\end {bmatrix} = \left[\begin{array}{ccc}-3&6&-9\\7&-1&0\\10&6&3\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right]

Which can be written as:

X' = \left[\begin{array}{ccc}-3&6&-9\\7&-1&0\\10&6&3\end{array}\right] X

where;

X' = \begin {bmatrix}   \dfrac{dx}{dt} \\ \\ \dfrac{dy}{dt} \\ \\ \dfrac{dz}{dt}\end {bmatrix}  \ \ \ \&   \ \ \  X = \left[\begin{array}{c}x\\y\\z\end{array}\right]

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Answer:

  • <em><u>0.126</u></em>

<em><u></u></em>

Explanation:

<u>1. Determine the percent of people who developed dementia from the entire population. </u>

a)<u> From the percent of people who had depression</u>:

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b) <u>From the number of people who did not have depression</u>:

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c) <u>Total percent:</u>

  • 2.2% + 15.3% 17.5% of all people developed dementia.

<u>2. Probability that the person suffered from depression earlier in life, if a person has developed dementia:</u>

  • percent of people who developed dementia and had depression / percent of people who developed dementia = 2.2% / 17.5% = 0.126

Note, that this can be calculated using the formula for conditional probability:

  • P(A/B) = P(A∩B) / P(B)

Where:

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  • P(B) = 22% × 10% + 17% × 90% = 17.5% = 0.175

  • P(A/B) = P(A∩B) / P(B) = 0.022 / 0.175 = 0.126
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Answer:

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Answer:

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