| 1. | The second step is to solve these independent equations one by one.
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| 2. | This is done by means of the following independent equations:
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| 3. | These are 6 independent equations relating stresses and strains.
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| 4. | Alternatively, the solution can be found by jointly solving any two independent equations.
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| 5. | These are 6 independent equations relating strains and displacements with 9 independent unknowns ( strains and displacements ).
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| 6. | Equivalently, if a system has more independent equations than unknowns, it is inconsistent and has no solutions.
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| 7. | Although there appear to be 64 equations in Faraday-Gauss, it actually reduces to just four independent equations.
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| 8. | Four unknowns cannot be found given two independent equations in these unknown variables and hence the beam is statically indeterminate.
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| 9. | In keeping with the idea that they usually represent time, their special significance vanishes in the time-independent equation.
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| 10. | The number of independent equations in the original system is the number of non-zero rows in the echelon form.
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