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

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

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. If A = [[1,0,1],[0,1,2],[0,0,4]] then show that |3A| = 27|A|

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Prove that: |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+z...

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  20. Prove that: |[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]|=(5x+4)(4-x)^2.

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