Display the data in matrix [tex]$W$[/tex] with rows indicating workers. What is element [tex]$w_{22}$[/tex]?
Answer (1)
Create a matrix W from the given data, where rows represent workers and columns represent months.
Identify the element w 22 in the matrix, which is the element in the second row and second column.
Read the value of w 22 from the matrix.
The element w 22 is 24 .
Explanation
Understanding the Problem The table provides the number of lawns mowed by Frank, Carl, and Vinny during June, July, and August. We need to represent this data in a matrix W where the rows correspond to the workers and the columns correspond to the months. Then, we need to identify the element w 22 of this matrix.
Constructing the Matrix We will create a 3x3 matrix W where the rows represent the workers (Frank, Carl, Vinny) and the columns represent the months (June, July, August). The elements of the matrix will be the number of lawns mowed by each worker in each month.
Identifying the Element Based on the table, the matrix W is: W = [ 28 21 19 17 24 15 22 29 17 ] The element w 22 is the element in the second row and second column, which corresponds to the number of lawns mowed by Carl in July.
Finding the Value From the matrix W , we can see that w 22 = 24 .
Examples
Matrices are useful for organizing data in various fields. For example, in economics, a matrix can represent the sales of different products by different stores. In computer graphics, matrices are used to perform transformations such as rotation and scaling of objects. In this case, the lawn-mowing data is organized in a matrix to easily see how many lawns each worker mowed each month. This can help the business owner analyze performance and make decisions about resource allocation.
