The numbers of calories burned by individuals of different...

The numbers of calories burned by individuals of different body weights while performing different types of exercises for a one-hour time period are represented by $A.$ $A=\left[ \begin{array}{cc}{472} & {563} \\ {590} & {704} \\ {177} & {211}\end{array}\right]$ (a) $\mathrm{A} 130$ -pound person and a 155 -pound person played basketball for 2 hours, jumped rope for 15 minutes, and lifted weights for 30 minutes. Organize the times spent exercising in a matrix $B$ (b) Compute $B A$ and interpret the result.

The numbers of calories burned by individuals of different body weights while performing different types of exercises for a one-hour time period are represented by $A.$
$A=\left[ \begin{array}{cc}{472} & {563} \\ {590} & {704} \\ {177} & {211}\end{array}\right]$
(a) $\mathrm{A} 130$ -pound person and a 155 -pound person played basketball for 2 hours, jumped rope for 15 minutes, and lifted weights for 30 minutes. Organize the times spent exercising in a matrix $B$
(b) Compute $B A$ and interpret the result.

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Key Concepts

Matrix Representation

This concept involves organizing data into rows and columns within a matrix structure. In many real-world applications, matrices can be used to represent complex data sets in a compact form, such as the calorie burn rates for various exercises across different body weights, or the time spent on each activity. The structured format facilitates efficient computation and interpretation of the data.

Matrix Multiplication

Matrix multiplication is the process of combining two matrices to produce a third matrix, where each element is calculated as the sum of the products of corresponding elements from rows of the first matrix and columns of the second matrix. In this context, multiplying a matrix of time durations by a matrix of calorie rates yields a new matrix whose elements represent the total calories burned for each body weight category across multiple exercise types.

Interpreting the Matrix Product

Interpreting the result of a matrix multiplication involves understanding how the computed values relate to the original data. In applied scenarios, such as calculating calories burned from different workouts, each entry in the resulting matrix sums up the contributions from each exercise type, providing a comprehensive measure of energy expenditure for individuals with specific characteristics.

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