# Application of matrix multiplication.

The concept of matrix multiplication is widely applied in day-to-day arithmetic. The following examples illustrate the application of matrix
multiplication.

Example

Solution

Solution

1. Jack went to buy 3 pencils, 2 rulers and 4 ball point pens. Okot went to buy 1 pencil, 1 ruler and 8 ball point pens. In Gulu, pencils and rulers
cost shs 60 each and ballpoint pen costs shs 20 each. In Pader, pencils and rulers cost shs 80 each and ballpoint pen costs shs 30 each.

Form the above items of jack and Okot as a 2×3 matrix and the cost in two towns as a 3×2 matrix; find the cost of items in:
i) Gulu

1. Peter when shopping and bought 5 books (B) for shs 100 each, 3 rubber (R) for shs 50 each and 10 pens (P) for shs 200 each. How much
money did Peter spend?

Solution
The items Peter bought can be written as row matrix as below.

The cost of the items is written as a column matrix.

The amount Peter spent

1. In the football league, a win (W) earns 3 points, a draw (D) only 1point and a loss (L) 0 point. The results for two football clubs in the English
premier league, Man U and Arsenal are given in the following table.

Use matrix multiplication to find the number of points each scored.

The matrix from the above information is

The number of points for W, D, and L can be written as a column matrix as

Thus, Man U scored 38 points and Arsenal scored 30 points.

1. Jane wants to go shopping and buy 3 writing pads (W), 4 exercise books (B) and 5 ball pens (P). Her sister Eva wants to buy 2 writing
pads, 6 exercise books and 3 ball pens. In Entebbe (E), writing pads cost shs 800, exercise books cost shs 300, and ball pens cost shs 150
each. In Kampala (K), writing pads cost shs 700, exercise books cost shs 500, and ball pens cost shs 100 each. Use matrix multiplication to find out where it is better to shop from.
Solution
The items Jane and Eva want can be shown in a 2 x 2 matrix

Their costs can be shown in a 3x 2 matrix

We multiply them together thus:

Jane would spend shs 4350 in Entebbe and shs 4600 in Kampala
Eva would spend shs 4450 in Entebbe and shs 5700 in Kampala