Mathematics · Linear Algebra and Differential Calculus
For 1 ≤ i, j ≤ n, let aij: &mathbb;R;→&mathbb;R; be differentiable functions with derivatives a'ij. Define f: &mathbb;R;→Mn(&mathbb;R;) and f': &mathbb;R;→Mn(&mathbb;R;) by f(t) = (aij(t))1≤i,j≤n and f'(t) = (a'ij(t))1≤i,j≤n. Suppose f(t) is an orthogonal matrix for all t ∈ &mathbb;R; and f(0) = In, the identity matrix of order n. Then:
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- 1f'(0) is skew-symmetric✓
- 2f'(0) is symmetric
- 3f'(0) is orthogonal
- 4f'(0) has determinant zero
Correct answer
f'(0) is skew-symmetric
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