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Without expanding prove that: |[x+y, y...

Without expanding prove that: `|[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=0` .

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Show that |[b-c,c-a, a-b],[ c-a, a-b,b-c],[ a-b,b-c,c-a]| = 0 .

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  2. Show that |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b ,c(a+b)]|=0 .

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  3. Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=...

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  4. Without expanding show that: =|[cose c^2theta,cot^2theta,1],[cot^2th...

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  5. Find the value of the determinant =|(2, 3, 4) ,(5, 6, 8),( 6x,9x, 12...

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  6. Without expanding show that |b^2c^2 bc b+cc^2a^2 ca c+a a^2b^2a b a+...

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  7. Without expanding evaluate the determinant |sinalphacosalphasin(alp...

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  8. Without expanding evaluate the determinant |(a^x+a^-x)^2(a^x-a^-x)^2 1...

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  9. If a ,\ b ,\ c are in A.P., find the value of |(2y+4, 5y+7, 8y+a),(3...

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  10. Without expanding evaluate the determinant =|(265, 240, 219), (240, ...

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  11. If D1=|1 1 1 x^2 y^2 z^2 x y z| and D2=|1 1 1y z z xx y x y z| , with...

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  12. Let D=|Ax x^2 1 By y^2 1 Cz z^2 1| and D1=|A B C x y z yz zx xy| ...

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  13. If A=|[a, b, c],[ x, y, z],[ p, q, r]| and B=|[q, -b, y],[ -p, a, -x...

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  14. If A is a skew-symmetric matrix of odd order n , then |A|=O .

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  15. Prove that: |[0,a,-b],[-a,0,-c],[ b, c,0]|=0 .

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  16. Without expanding or evaluating show that |(0,b-a, c-a),( a-b,0,c-b)...

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  17. Without expanding, prove that |(a+b x, c+dx, p+q x), (a x+b, c x+d, ...

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  18. Prove that: |-a^2 ab ac ba -b^2 bc ...

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  19. Prove that: |(1, 1, 1),( 1, 1+x,1) ,(1, 1, 1+y)|=x y .

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  20. Evaluate: |(1,a ,a^2), (1,b,b^2) ,(1,c,c^2)| .

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