### Home > PC3 > Chapter 9 > Lesson 9.1.1 > Problem9-8

9-8.

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.

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

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}}

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

$\begin{bmatrix}3(6) & 3(1) & 3(5)\\3(3) & 3(1.5) & 3(4)\end{bmatrix}$

1. 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.

Compute $LC$.

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