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Prove that |(1, a, a^3),(1, b, b^3),(1, ...

Prove that `|(1, a, a^3),(1, b, b^3),(1, c, c^3)|`= (a-b)(b-c)(c-a)(a+b+c).

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ARIHANT PUBLICATION-DETERMINANTS -PART -1 QUESTION FOR PRACTICE
  1. Solve for x, |{:(15-2x,11,10),(11-3x,17,16),(7-x,14,13):}|=0

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  2. IF cos 2 theta=0 then simplify |{:(0,cos theta, sin theta),(cos theta,...

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  3. Prove that |(1, a, a^3),(1, b, b^3),(1, c, c^3)|= (a-b)(b-c)(c-a)(a+b+...

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  4. using the properties of determinants prove that |{:(1,x+y,x^2+y^2),(...

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  5. Using properties of determinants prove that |{:(a^2+2a,2a+1,1),(2a+1...

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  6. Prove that the following. [[(a+1)(a+2),a+2,1],[(a+2)(a+3),a+3,1],[(a+3...

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  7. Using properties of determinants solve the following for x, |{:(x+a,x,...

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  8. Solve [[a+x,a-x,a-x],[a-x,a+x,a-x],[a-x,a-x,a+x]]=0

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  9. IF |{:(4-x,4+x,4+x),(4+x,4-x,4+x),(4+x,4+x,4-x):}|=0 then find the val...

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  10. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

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  11. Using properties of determinant prove that |{:(alpha,beta,gamma),(alph...

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  12. IF a,b and c are real numbers and Delta=|{:(b+c,c+a,a+b),(c+a,a+b,b+c)...

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  13. Using the properties of determinants prove that |{:(a+b+2c,a,b),(c,b...

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  14. Find the value of x if |(2x,3),(1,x)|=|(3,4),(-1,2)|

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  15. Prove that |[x+y, x, x],[5x+4y, 4x, 2x], [10x+8y, 8x, 3x]|=x^3

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  16. If x,y and z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),...

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  17. Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c]...

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  18. Show that Delta =Delta1 where Delta=|{:(Ax,x^2,1),(By,y^2,1),(Cz,z^2...

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  19. IFDelta=|{:(1,x,x^2),(1,y,y^2),(1,z,z^2):}| and Delta1=|{:(1,1,1),(yz,...

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  20. Using properties of determinants, prove that |{:(y^2z^2,yz,y+z),(z^2x^...

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