Shola’s Bakery uses sugar, eggs, and butter in all of its cakes, as well as in the frosting. Matrix $C$ shows how many eggs, cups of sugar, and ounces of butter are used in each angel food cake and in each devil’s food cake. Matrix $F$ shows how many eggs, cups of sugar, and ounces of butter are used in the frosting for each cake.

$C = {\begin{aligned}[c] \text{e s b} \; \; \,\\ \begin{array}{l} \text {af}\\ \text {df} \end{array} \quad \left[\begin{array}{&c&c&c} 6 & 1 & 5 \\ 3 & 1.5 & 4 \end{array}\right] \end{aligned}}$

1. Write the matrix $C + F,$ being sure to label the rows and columns, and explain what it represents.

   Step (a):

   $\begin{bmatrix}6+2 & 1+1 & 5+2\\3+1 & 1.5+2 & 4+4\end{bmatrix}$

$F = {\begin{aligned}[c] \text{e s b}\;\;\,\\ \begin{array}{l} \text {af}\\ \text {df} \end{array} \quad \left[\begin{array}{&c&c&c} 2 & 1 & 2 \\ 1 & 2 & 4 \end{array}\right] \end{aligned}}$

3. Leora orders three angel food cakes and two devil’s food cakes both without frosting, as represented by the matrix $L$ at right. Use matrix multiplication to write a matrix that shows how much sugar, eggs, and butter Shola will need to fill Leora’s order. Show all of your work.

   Hint (c):

   Compute $LC$.

$\begin{array}{l} \qquad \;\; \text{af} \quad \;\;\text{df} \\ L = \left[\;3 \qquad 2\;\right] \end{array}$