Mathematics: Keith takes 12 hours to clean the store, and mike takes 10 hours to finish the job. how hong will they take together?

Keith takes 12 hours to clean the store, and mike

Ответ:

kay20081

06.05.2023

$= \left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right] = x_2 \left[\begin{array}{ccc}2\\1\\0\end{array}\right] + x_3 \left[\begin{array}{ccc}-3\\0\\1\end{array}\right]$

Step-by-step explanation:

Given: 3x1 - 6x2 + 9x3 = 0

x2 and x3 are free variables

We have:

3x1 = 6x2 - 9x3

divide all sides by 3, we have:

x1 = 2x2 - 3x3

Finding the general solution, we have:

$\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right] = \left[\begin{array}{ccc}2x_2 - 3x_3\\x_2\\x_3\end{array}\right]$

$= \left[\begin{array}{ccc}2x_2\\x_2\\0\end{array}\right] + \left[\begin{array}{ccc}-3x_3\\0\\x_3\end{array}\right]$

$= x_2 \left[\begin{array}{ccc}2\\1\\0\end{array}\right] + x_3 \left[\begin{array}{ccc}-3\\0\\1\end{array}\right]$

The general solution is

$= \left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right] = x_2 \left[\begin{array}{ccc}2\\1\\0\end{array}\right] + x_3 \left[\begin{array}{ccc}-3\\0\\1\end{array}\right]$

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Keith takes 12 hours to clean the store, and mike takes 10 hours to finish the job. how hong will they take together?

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