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Problem

[[8/3],[8/3],[8/3]]+[[−19/14],[57/28],[−19/28]]

Solution

1. Identify the operation as vector addition, which requires adding corresponding components of the two vectors.

2. Set up the addition for each component:

8/3+(−19/14)

8/3+57/28

8/3+(−19/28)

3. Find a common denominator for the first component. The least common multiple of 3 and 14 is 42

(8⋅14)/(3⋅14)−(19⋅3)/(14⋅3)=112/42−57/42=55/42

4. Find a common denominator for the second and third components. The least common multiple of 3 and 28 is 84

(8⋅28)/(3⋅28)+(57⋅3)/(28⋅3)=224/84+171/84=395/84

(8⋅28)/(3⋅28)−(19⋅3)/(28⋅3)=224/84−57/84=167/84

5. Combine the results into a single vector.

Final Answer

[[8/3],[8/3],[8/3]]+[[−19/14],[57/28],[−19/28]]=[[55/42],[395/84],[167/84]]

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