### 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.

 e      s      b $C=$ afdf $\left[ \begin{array} { c c c } { 6 } & { 1 } & { 5 } \\ { 3 } & { 1.5 } & { 4 } \end{array} \right]$
1. Write the matrix $C + F,$ being sure to label the rows and columns, and explain what it represents.

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

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

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

 e       s      b $F=$ afdf $\left[ \begin{array} { c c c } { 2 } & { 1 } & { 2 } \\ { 1 } & { 2 } & { 4 } \end{array} \right]$
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 $LC$.

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