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Prove that triangle = |[a+bx,c+dx,p+qx],...

Prove that `triangle = |[a+bx,c+dx,p+qx],[ax+b,cx+d,px+q],[u,v,w]| = (1-x^2)|[a,c,p],[b,d,q],[u,v,w]|`

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PSEB-DETERMINANTS-Exercise
  1. Prove that triangle = |[a+bx,c+dx,p+qx],[ax+b,cx+d,px+q],[u,v,w]| = (1...

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

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  3. Evaluate the determinant: |[costheta,-sintheta],[sintheta,costheta]|

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  4. Evaluate the determinant : |[x^2-x+1,x+1],[x+1,x+1]|

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  5. If A = [[1,2],[4,2]], then show that |2A| = 4|A|

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

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  7. Evaluate the determinant : |[3,-1,-2],[0,0,-1],[3,-5,0]|

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

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

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  10. Evaluate the determinant : |[2,-1,-2],[0,2,-1],[3,-5,0]|

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  11. If A = [[1,1,-2],[2,1,-3],[5,4,-9]], find |A|

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

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  13. Find values of x, if : |[2,3],[4,5]| = |[x,3],[2x,5]|

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

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

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

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

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

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