alleryStart learning →Closed-form normal equations require XᵀX to be
AHave negative determinant
BSingular
CInvertible (i.e., X has full column rank — no perfectly collinear features)
DDiagonal
Answer & Solution
Correct answer: C. Invertible (i.e., X has full column rank — no perfectly collinear features)
If XᵀX is singular (features collinear or n < d), the inverse doesn't exist.
**Practical fix:** ridge regression θ = (XᵀX + λI)⁻¹ Xᵀy, which is always invertible for λ > 0.
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