Answer:
Step-by-step explanation:
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Answer:
I think it is C that would be the best answer
Option D:
![\left[\begin{array}{l}x_{1} \\x_{2}\end{array}\right]=\left[\begin{array}{cc}0.5 & -3 \\0 & 1\end{array}\right]\left[\begin{array}{c}2 \\-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bl%7Dx_%7B1%7D%20%5C%5Cx_%7B2%7D%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.5%20%26%20-3%20%5C%5C0%20%26%201%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%20%5C%5C-3%5Cend%7Barray%7D%5Cright%5D)
Solution:
Given equation:
![\left[\begin{array}{ll}2 & 6 \\0 & 1\end{array}\right]\left[\begin{array}{l}x_{1} \\x_{2}\end{array}\right]=\left[\begin{array}{l}2 \\-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bll%7D2%20%26%206%20%5C%5C0%20%26%201%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bl%7Dx_%7B1%7D%20%5C%5Cx_%7B2%7D%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bl%7D2%20%5C%5C-3%5Cend%7Barray%7D%5Cright%5D)
where
,
, ![B =\left[\begin{array}{l}2 \\-3\end{array}\right]](https://tex.z-dn.net/?f=B%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bl%7D2%20%5C%5C-3%5Cend%7Barray%7D%5Cright%5D)
This is in the form of AX = B.
To solve this equation.
Multiply by
on both sides.


To find
using matrix formula:
![$\left[\begin{array}{ll}a & b \\c & d\end{array}\right]^{-1}=\frac{1}{a d-b c}\left[\begin{array}{cc}d & -b \\-c & a\end{array}\right]](https://tex.z-dn.net/?f=%24%5Cleft%5B%5Cbegin%7Barray%7D%7Bll%7Da%20%26%20b%20%5C%5Cc%20%26%20d%5Cend%7Barray%7D%5Cright%5D%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7Ba%20d-b%20c%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dd%20%26%20-b%20%5C%5C-c%20%26%20a%5Cend%7Barray%7D%5Cright%5D)
![$\left[\begin{array}{ll}2 & 6 \\0 & 1\end{array}\right]^{-1}=\frac{1}{2\times1- 6\times0}\left[\begin{array}{cc}1 & -6 \\0 & 2\end{array}\right]](https://tex.z-dn.net/?f=%24%5Cleft%5B%5Cbegin%7Barray%7D%7Bll%7D2%20%26%206%20%5C%5C0%20%26%201%5Cend%7Barray%7D%5Cright%5D%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7B2%5Ctimes1-%206%5Ctimes0%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%20%26%20-6%20%5C%5C0%20%26%202%5Cend%7Barray%7D%5Cright%5D)
![$=\frac{1}{2}\left[\begin{array}{cc}1 & -6 \\0 & 2\end{array}\right]](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B2%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%20%26%20-6%20%5C%5C0%20%26%202%5Cend%7Barray%7D%5Cright%5D)
Multiply
into inside the matrix.
![$=\left[\begin{array}{cc}\frac{1}{2} & \frac{-6}{2} \\\frac{0}{2} & \frac{2}{2} \end{array}\right]](https://tex.z-dn.net/?f=%24%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B1%7D%7B2%7D%20%20%26%20%5Cfrac%7B-6%7D%7B2%7D%20%20%5C%5C%5Cfrac%7B0%7D%7B2%7D%20%20%26%20%5Cfrac%7B2%7D%7B2%7D%20%5Cend%7Barray%7D%5Cright%5D)
![=\left[\begin{array}{cc}0.5 & -3 \\0 & 1\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.5%20%26%20-3%20%5C%5C0%20%26%201%5Cend%7Barray%7D%5Cright%5D)
Substitute into
, we get
![\left[\begin{array}{l}x_{1} \\x_{2}\end{array}\right]=\left[\begin{array}{cc}0.5 & -3 \\0 & 1\end{array}\right]\left[\begin{array}{c}2 \\-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bl%7Dx_%7B1%7D%20%5C%5Cx_%7B2%7D%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.5%20%26%20-3%20%5C%5C0%20%26%201%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%20%5C%5C-3%5Cend%7Barray%7D%5Cright%5D)
This equation can be used to solve the given matrix.
Option D is the correct answer.
You have to find the mean:
34+99=133
133 divided by 2 = 66.5
So your answer is 66.5
(Mean means average)
The value of 8 if it we're in the thousands place would be 8,000.