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Introduction to Imperfections in Solids

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What is the maximum number of different elements required to form a symmetric matrix of order 12?

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Solution

$M a t r i x o f o r d e r 12 r e q u i r e 12 \times 12 = 144 e l e m e n t s . 12 e l e m e n t s f o r i = j (d i a g o n a l e l e m e n t s) 66 e l e m e n t s f o r i < j w h i c h a r e e q u a l t o 66 e l e m e n t s f o r i > j H e n c e, M a x i m u m n u m b e r o f d i f f e r e n t e l e m e n t s r e q u i r e d a r e 66 + 12 = 78$

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