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If A =[{:(1,2),(4,2):}], then show that ...

If `A =[{:(1,2),(4,2):}]`, then show that `| 2A| = 4|A|`.

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Evaluate the determinants in exercises 1 to 2. |(cos theta, - sin th...

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  2. Evaluate the following determinants: {:|(x^2-x+1,x-1),(x+1,x+1)|

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  3. If A =[{:(1,2),(4,2):}], then show that | 2A| = 4|A|.

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  4. If A = [[1,0,1],[0,1,2],[0,0,4]] then show that |3A| = 27|A|

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

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  6. Evaluate the determinant : |[3,-4,5],[1,1,-2],[2,3,1]|

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  7. Evaluate the determinant : |[0,1,2],[-1,0,-3],[-2,3,0]|

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  8. Evaluate the determinant Delta = abs{:(2,-1,-2),(0,2,-1),(3,-5,0):}.

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  9. If A = [{:(1,1,-2),(2,1,-3),(5,3,-9):}], find |A|.

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  10. Find values of x, if : |[2,4],[5,1]| = |[2x,4],[6,x]|

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  11. Find the value of x, if |{:(2,3),(4,5):}|=|{:(x,3),(2x,5):}|.

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  12. If |[x,2],[18,x]| = |[6,2],[18,6]|, then x is equal to:

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  13. Using the property of determinants and without expanding , prove that:...

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  14. Using the property of determinants and without expanding , prove that:...

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  15. Using the property of determinants and without expanding , prove that:...

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  16. Using the property of determinants and without expanding , prove that:...

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  17. Using the property of determinants and without expanding prove that : ...

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  18. By using properties of determinants, Show that : {:|(0,a,-b),(-a,0,-...

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  19. Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

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  20. By using properties of determinants, show that : |[1,a,a^2],[1,b,b^2]...

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