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In a SYMMETRIC laminate the inverse relations have the form: {ε°} = a·{N}, {κ} = d·{M}, where a and d are inverses of A and D. The off-diagonal element $a_{11}$ in terms of A entries is:
A{'text': '$a_{11} = A_{11}$', 'label': 'A'}
B{'text': '$a_{11} = (A_{22}A_{66} - A_{26}^2)/\\det A$', 'label': 'B'}
C{'text': '$a_{11} = 1/A_{11}$', 'label': 'C'}
D{'text': '$a_{11} = 0$', 'label': 'D'}
Answer & Solution
Correct answer: B. {'text': '$a_{11} = (A_{22}A_{66} - A_{26}^2)/\\det A$', 'label': 'B'}
For a symmetric 3×3 matrix, the inverse element $a_{11}$ is the (1,1)-cofactor divided by determinant: $(A_{22}A_{66} - A_{26}^2)/\det A$. Other entries follow analogous cofactor formulas.
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