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The first matrix (A) shows the number of cars and bicycles owned by two families.  The second matrix (B) records the wheels and seats for cars and bicycles.

Use a matrix product to find a matrix that gives the number of wheels and seats owned by each family.

A =

CarsBicycles
Smith23
Jones14

B =

WheelsSeats
Car45
Bicycle21

(Matrices are in tables as I cant make matrices)

May 10, 2020
edited by MathsLlama  May 11, 2020

#1
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The first matrix (A) shows the number of cars and bicycles owned by two families.

The second matrix (B) records the wheels and seats for cars and bicycles.

Use a matrix product to find a matrix that gives the number of wheels and seats owned by each family.

$$\begin{array}{|c|c|c|} \hline A & \text{Cars} & \text{ Bicycles } \\ \hline \text{Smith} & 2 & 3 \\ \hline \text{Jones} & 1 & 4 \\ \hline \end{array} \begin{array}{|c|c|c|} \hline B & \text{Wheels} & \text{ Seats } \\ \hline \text{Car} & 4 & 5 \\ \hline \text{Bicycle} & 2 & 1 \\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline A \times B &=& \left( \begin{array}{cc} 2 & 3 \\ 1 & 4 \\ \end{array}\right) \times \left(\begin{array}{cc} 4 & 5 \\ 2 & 1 \\ \end{array}\right) \\ &=& \left(\begin{array}{cc} 14 & 13 \\ 12 & 9 \\ \end{array}\right) \\ \hline \end{array}$$

$$\begin{array}{|c|c|c|} \hline A\times B & \text{Wheels} & \text{ Seats } \\ \hline \text{Smith} & 14 & 13 \\ \hline \text{Jones} & 12 & 9 \\ \hline \end{array}$$ May 11, 2020