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Questo esame si sostiene in inglese: le lezioni e le domande sono in inglese. L'interfaccia resta in italiano.
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Key formulas
2×2 Determinant
For A = [[a,b],[c,d]]. Zero determinant means no unique solution.
2×2 Matrix Inverse
Swap the diagonal, negate the off-diagonal, divide by the determinant.
Characteristic Equation
Eigenvalues λ are the solutions. For a diagonal matrix, they are just the diagonal entries.
Trace & Determinant Relations
Sum and product of eigenvalues — useful for quick verification.
Lagrangian
λ is the shadow price: how much the objective improves per unit relaxation of the constraint.
Part 1 of 1
For a 2×2 matrix A = [[a, b], [c, d]]:
If det(A) ≠ 0 → invertible, unique solution exists. If det(A) = 0 → singular, no unique solution.
Worked example
A = [[3, 1], [2, 4]]. det(A) = 12 − 2 = 10 ≠ 0 → invertible. A⁻¹ = (1/10)·[[4,−1],[−2,3]].
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