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The rule for multiplying matrices is essentially a generalization of the above reasoning.

To multiply matrices, it is not necessary that they be of the same order. The requirement is that the number of columns of the first matrix be the same as the number of rows of the second matrix. Matrices that satisfy this requirement are said ro be conformable for matrix multiplication.

Before we present the formal definition of matrix multiplication we will illustrate the idea by means of some examples.

Example 8.7 Total Revenue

Determine the revenue of a parking lot on a given Monday, Tuesday, and Wednesday based on the following data:

Number of cars Number of buses

Monday 30 5

Tuesday 25 5

### Wednesday 35 15

The dollar charge per vehicic is $4 for cars, and S8 for buses. The daily revenue in dollars is m on Monday, / on Tuesday, and w on Wednesday. In matrix notation this information can be put as

Monday vector Tuesday vector Wednesday vector

Charge vector

Solution

To obtain m, we need to calculate

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