How do you perform vector addition using column coordinates?
Conditions
- Vectors have established coordinate representations.
- The vectors must have the same dimension and basis.
Reasoning, step by step
- Write down the column vectors for each vector.
- Add the top entries together to get the top entry of the result.
- Add the bottom entries together to get the bottom entry of the result.
- Combine these sums into a new column vector.
Example
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Common misconceptions
- Adding all components together into a single scalar.
- Multiplying the components instead of adding them.
- Assuming this works for vectors of different dimensions.
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