Complete Question: The complete question is in the file attached to this solution
Answer:
a) ![\left[\begin{array}{ccc}45&24\\67&89\end{array}\right] =\left[\begin{array}{ccc}X_{1} \\X_{2} \end{array}\right] + \left[\begin{array}{ccc}155.25 \\397.80 \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D45%2624%5C%5C67%2689%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7DX_%7B1%7D%20%5C%5CX_%7B2%7D%20%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D155.25%20%5C%5C397.80%20%5Cend%7Barray%7D%5Cright%5D)
b) The new hire sold a small drink for $1.78 and a medium drink for $3.13
Step-by-step explanation:
The matrix vector equation can be written as:
............(1)
let X₁ = Price of small drinks
Let X₂ = Price of medium drinks
The vector
of the prices of small and medium drinks is:
![\bar{X} = \left[\begin{array}{ccc}X_{1} \\X_{2} \end{array}\right]](https://tex.z-dn.net/?f=%5Cbar%7BX%7D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7DX_%7B1%7D%20%5C%5CX_%7B2%7D%20%5Cend%7Barray%7D%5Cright%5D)
The matrix of the total sales can be written as:
![A = \left[\begin{array}{ccc}45&24\\67&89\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D45%2624%5C%5C67%2689%5Cend%7Barray%7D%5Cright%5D)
![B = \left[\begin{array}{ccc}155.25 \\397.80 \end{array}\right]](https://tex.z-dn.net/?f=B%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D155.25%20%5C%5C397.80%20%5Cend%7Barray%7D%5Cright%5D)
According to the equation written in (1), the matrix vector equation is:
![\left[\begin{array}{ccc}45&24\\67&89\end{array}\right] =\left[\begin{array}{ccc}X_{1} \\X_{2} \end{array}\right] + \left[\begin{array}{ccc}155.25 \\397.80 \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D45%2624%5C%5C67%2689%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7DX_%7B1%7D%20%5C%5CX_%7B2%7D%20%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D155.25%20%5C%5C397.80%20%5Cend%7Barray%7D%5Cright%5D)
![45X_{1} + 24X_{2} = 155.25\\67X_{1} + 89X_{2} = 397.80](https://tex.z-dn.net/?f=45X_%7B1%7D%20%2B%2024X_%7B2%7D%20%3D%20155.25%5C%5C67X_%7B1%7D%20%2B%2089X_%7B2%7D%20%3D%20397.80)
Solving for X₁ and X₂ in the equations above:
X₁ = 1.78
X₂ = 3.13