Exam-style question
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Let u = [2, 1] and v = [4, 3]. Calculate 2u + v. State what scalar-vector multiplication and vector addition achieve.
Model answer
What a good answer should say
- First multiply every entry of u by 2: 2u = [4, 2].
- Then add corresponding entries of v: 2u + v = [4, 2] + [4, 3] = [8, 5].
- Scalar-vector multiplication achieves scaling, while vector addition achieves translation.
Explanation
Why this works
Scalar multiplication applies the scalar to every vector entry. Vector addition then combines corresponding entries.
The specification associates scalar-vector multiplication with scaling and vector addition with translation.
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