Please help to solve and explain into details. Thank you. ### U.S. Army Personnel Data Analysis#### Question 3The following table illustrates the number of personnel (in thousands) in three branches of the U.S. Army in 2001, along with the subsequent changes in 2002 and 2003.| Year | Active Duty | Reserve | National Guard ||-----------------|-------------|---------|----------------|| 2001 | 75 | 35 | 60 || Change in 2002 | 5 | -15 | 2 || Change in 2003 | -12 | 5 | -17 |**Objective:**Utilize matrix algebra to determine the number of personnel in each branch for the years 2002 and 2003.**Detailed Explanation of the Table:**- **2001 Data:** Lists the initial number of personnel in each branch. - Active Duty: 75,000 - Reserve: 35,000 - National Guard: 60,000- **Changes in 2002:** Shows the increase or decrease in the number of personnel from 2001. - Active Duty increased by 5,000 - Reserve decreased by 15,000 - National Guard increased by 2,000- **Changes in 2003:** Indicates the increase or decrease in the number of personnel from 2002. - Active Duty decreased by 12,000 - Reserve increased by 5,000 - National Guard decreased by 17,000**Instructions:**Students are to employ matrix algebra techniques to calculate the number of personnel in each branch for the years:a. 2002b. 2003This exercise aims to enhance understanding and application of matrices in solving real-world data representation problems.

Active DutyReserveNational Guard2001753560Change in 20025-152Change in 2003-125-17

Answered: 3. The following table shows the number…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

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