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Without expanding evaluate the determina...

Without expanding evaluate the determinant `|(a^x+a^-x)^2(a^x-a^-x)^2 1(a^y+a^(-y))^2(a^y-a^(-y))^2 1(a^2+a^(-z))^2(a^z-a^(-z))^2 1|,` where `a , >0a n dx , y , z in Rdot`

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Without expanding evaluate the determinant |[(a^x+a^(-x))^2,(a^x-a^(-x))^2, 1],[(a^y+a^(-y))^2,(a^y-a^(-y))^2, 1],[(a^z+a^(-z))^2,(a^z-a^(-z))^2, 1]|, where a>0 and x , y , z in R

If a, b,c> 0 and x,y,z in RR then the determinant |((a^x+a^-x)^2,(a^x-a^-x)^2,1),((b^y+b^-y)^2,(b^y-b^-y)^2,1),((c^z+c^-z)^2,(c^z-c^-z)^2,1)| is equal to:

Without expanding, show that "Delta"=|(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|=2(a-b)(b-c)(c-a)(x-y)(y-z)(z-x)

Without expanding,FIND "Delta"=|(((a-x)^2),((a-y)^2),((a-z)^2)),(((b-x)^2),((b-y)^2),((b-z)^2)),(((c-x)^2),((c-y)^2),((c-z)^2))|

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

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

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

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

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

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  6. 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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  7. 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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  8. If A=|[a, b, c],[ x, y, z],[ p, q, r]| and B=|[q, -b, y],[ -p, a, -x...

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

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

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

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

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

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

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

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  16. Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z...

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  17. Prove that: |[alpha,beta,gamma],[alpha^2,beta^2,gamma^2],[beta+gamma,g...

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  18. In a triangleABC, if |(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB...

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  19. In a A B C ,if|1 1 1 1+cosA 1+cosB 1+cosC cos^2A+A cos^2B+cosB cos^2...

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  20. Show that |[a ,b ,c],[ a^2,b^2,c^2],[bc, ca, ab]|=|[1, 1, 1],[a^2,b^2,...

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