Answer
(a) $ \begin{bmatrix} 97 \\ 46.5 \\ 41 \end{bmatrix}$
(b) $\begin{bmatrix} 70 \\ 33.5 \\ 48.5 \end{bmatrix}$
(c) $ \begin{bmatrix} 220 & 110 & 90 \\75 & 45 & 50\\120 & 55 & 50 \end{bmatrix}$
(d) $ \begin{bmatrix} 167 \\ 80 \\ 89.5 \end{bmatrix}$
See explanations.
Work Step by Step
Identify the given matrices:
$ \begin{array}( \\A= \\ \\ \end{array} \begin{bmatrix} 120 & 50 & 60 \\40 & 25 & 30\\60 & 30 & 20 \end{bmatrix}$
$\begin{array}( \\B= \\ \\ \end{array} \begin{bmatrix} 100 & 60 & 30 \\35 & 20 & 20\\60 & 25 & 30 \end{bmatrix} $
$\begin{array}( \\C= \\ \\ \end{array} \begin{bmatrix} 0.1 \\ 0.5 \\ 1.0 \end{bmatrix} $
(a) $ \begin{array}( \\AC= \\ \\ \end{array} \begin{bmatrix} 120 & 50 & 60 \\40 & 25 & 30\\60 & 30 & 20 \end{bmatrix} \begin{bmatrix} 0.1 \\ 0.5 \\ 1.0 \end{bmatrix} \begin{array}( \\= \\ \\ \end{array} \begin{bmatrix} 97 \\ 46.5 \\ 41 \end{bmatrix}$
The result matrix gives the total sales for each person on Saturday. That is: sales for Amy 97, for Beth 46.5, and for Chad 41 dollars.
(b) $ \begin{array}( \\BC= \\ \\ \end{array} \begin{bmatrix} 100 & 60 & 30 \\35 & 20 & 20\\60 & 25 & 30 \end{bmatrix} \begin{bmatrix} 0.1 \\ 0.5 \\ 1.0 \end{bmatrix} \begin{array}( \\= \\ \\ \end{array} \begin{bmatrix} 70 \\ 33.5 \\ 48.5 \end{bmatrix}$
The result matrix gives the total sales for each person on Sunday. That is: sales for Amy 70, for Beth 33.5, and for Chad 48.5 dollars.
(c) Add the corresponding elements, we have
$ \begin{array}( \\A+B= \\ \\ \end{array} \begin{bmatrix} 220 & 110 & 90 \\75 & 45 & 50\\120 & 55 & 50 \end{bmatrix}$
The result matrix gives the number of each fruit sold for each person on both days.
(d) $ \begin{array}( \\(A+B)C= \\ \\ \end{array} \begin{bmatrix} 220 & 110 & 90 \\75 & 45 & 50\\120 & 55 & 50 \end{bmatrix} \begin{bmatrix} 0.1 \\ 0.5 \\ 1.0 \end{bmatrix} \begin{array}( \\= \\ \\ \end{array} \begin{bmatrix} 167 \\ 80 \\ 89.5 \end{bmatrix}$
The result matrix gives the total sales for each person on both days. That is: sales for Amy 167, for Beth 80, and for Chad 89.5 dollars.
