Mathematics · Linear Algebra
Which of the following functions defines a valid inner product over the real vector space &mathbb{R}2(&mathbb{R})?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1⟨(x1, y1), (x2, y2)⟩ = 2x1x2 + x1y2 + x2y1 + 2y1y2✓
- 2⟨(x1, y1), (x2, y2)⟩ = 4x1x2 + x1y2 + x2y1
- 3⟨(x1, y1), (x2, y2)⟩ = x12x22 + x1y2 + x2y1 + y12y22
- 4⟨(x1, y1), (x2, y2)⟩ = x1x2 + x1y2 + 4x2y1 + y1y2
Correct answer
⟨(x1, y1), (x2, y2)⟩ = 2x1x2 + x1y2 + x2y1 + 2y1y2
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