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.

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

   Hint (a):

   Add the numbers in the corresponding entries.

2. Write the matrix $3C$, with labels, and explain what it represents.

   Hint (b):

   Multiply each entry in matrix $C$ by $3$.

$C = {\begin{aligned}[c] \text{e s b} \; \; \,\\ \begin{array}{l} \text {af}\\ \text {df} \end{array} \quad \left[\begin{array}{&c&c&c} 6 & 1 & 5 \\ 3 & 1.5 & 4 \end{array}\right] \end{aligned}}\\ \\ \\ F = {\begin{aligned}[c] \text{e s b} \; \; \,\\ \begin{array}{l} \text {af}\\ \text {df} \end{array} \quad \left[\begin{array}{&c&c&c} 2 & 1 & 2 \\ 1 & 2 & 4 \end{array}\right] \end{aligned}}$

3. Leora orders three angel food cakes and two devil's food cakes 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.

$L = {\begin{aligned}[l] {af \quad df } \\ \left[\begin{array}{l l} 3 & 2 \\ \end{array}\right] \end{aligned}}$