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Evaluate the following determinants |{...

Evaluate the following determinants
`|{:(1,x,x),(0,sinx,siny),(0,cosx,cosy):}|`

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The correct Answer is:
`sin(x-y)`
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ARIHANT PUBLICATION-DETERMINANTS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS (EXERCISE 5(A))
  1. Evaluate the following determinants |{:(1,0,0),(0,1,0),(0,0,1):}|

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  2. Evaluate the following determinants |{:(2,3,1),(0,0,0),(-1,2,0):}|

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  3. Evaluate the following determinants |{:(1,x,x),(0,sinx,siny),(0,cosx...

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  4. Evaluate the following determinants |{:(1,2,3),(1,2,3),(3,4,5):}|

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  5. Evaluate the following determinants |{:(0.2,0.1,3),(0.4,0.2,7),(0.6,...

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  6. Evaluate the following determinants. [[1,omega,omega^2],[omega,omega^2...

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  7. Evaluate the following determinants |{:(1,1,1),(2,2,2),(3,3,3):}|

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  8. Evaluate the following determinants |{:(-6,0,0),(3,-5,7),(2,8,11):}|

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  9. Evaluate the following determinants |{:(1,0,0),(2,3,5),(4,1,3):}|

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  10. Evaluate the following determinants |{:(-18,17,19),(3,0,0),(-14,5,2)...

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  11. State true or false. If the first and second rows of a determinant be ...

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  12. State true or false. If first and third rows of a determinant be inter...

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  13. State true or false. If in a third order determinant first row be chan...

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  14. State true or false. A row and a column of a determinant can have two ...

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  15. State true or false. The minor and the co-factor of the element a32 of...

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  16. State true of false. [[3,1,3],[0,4,0],[1,3,1]]=0

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  17. State True or False abs((6,4,2),(4,0,7),(5,3,4))=abs((6,4,5),(4,0,3)...

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  18. State true of false. [[2,3,4],[5,6,7],[1,2,3]]=[[4,2,3],[7,5,6],[3,1,2...

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  19. What is the value of |[0,8,0],[25,520,25],[1,410,0]|?

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  20. IF omega is cube root of unity, then |{:(1,omega,omega^2),(omega,omega...

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