3. The following table shows the number of personnel, in thousands, in three brances of the U.S. Army in 2001, and the changes in 2002 and 2003. Active Duty Reserve National Guard 2001 75 5 Change in 2002 Change in 2003 -12 Use matrix algebra to find the number of personnel in each branch a. 2002 and b. 2003. 35 -15 5 60 2 -17
3. The following table shows the number of personnel, in thousands, in three brances of the U.S. Army in 2001, and the changes in 2002 and 2003. Active Duty Reserve National Guard 2001 75 5 Change in 2002 Change in 2003 -12 Use matrix algebra to find the number of personnel in each branch a. 2002 and b. 2003. 35 -15 5 60 2 -17
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Transcribed Image Text:### U.S. Army Personnel Data Analysis
#### Question 3
The 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. 2002
b. 2003
This exercise aims to enhance understanding and application of matrices in solving real-world data representation problems.
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