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Prove that |y z-x^2z x-y^2x y-z^2z x-y^2...

Prove that `|y z-x^2z x-y^2x y-z^2z x-y^2x y-z^2y z-x^2x y-z^2y z-x^2z x-y^2|` is divisible by `(x+y+z),` and hence find the quotient.

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The correct Answer is:
`(x+y+z)(xy+yz+zx-x^(2)-y^(2)-z^(2))^(2)`
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CBSE COMPLEMENTARY MATERIAL-MATRICES AND DETERMINANTS-SIX MARK QUESTIONS
  1. Prove that |y z-x^2z x-y^2x y-z^2z x-y^2x y-z^2y z-x^2x y-z^2y z-x^2z ...

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  2. Using elementary tansformations, find the inverse of the matrix A=[(...

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  3. Using matrix method, solve the system of linear equations x-2y=10,2x...

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  4. Find A^(-1) if A=|(0,1,1),(1,0,1),(1,1,0)| and show that A^(-1)=(A^(2)...

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  5. Find the matrix x for which [(3,2),(7,5)]x[(-1,1),(-2,1)]=[(2,-1),(0,4...

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  6. Let A=[2 3-1 2] and f(x)=x^2-4x+7 . Show that f(A)=O . Use this result...

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  7. If a+b+c=0and|(a-x,c,b),(c,b-x,a),(b,a,c-x)|=0, then show that either ...

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  8. If A+B+C=pi, then value of |{:(sin(A+B+C),sinB,cosC),(-sinB,0,tanA),(c...

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  9. |((x-2)^2,(x-1)^2,x^2),((x-1)^2,x^2,(x+1)^2),(x^2,(x+1)^2,(x+2)^2)|=-8...

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  10. Prove |[-bc, b^2+bc, c^2+bc] , [a^2+ac, -ac, c^2+ac] , [a^2+ab, b^2+ab...

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  11. Prove that: |(a,a+c,a-b),(b-c,b,b+a),(c+b,c-a,c)|=(a+b+c)(a^(2)+b^(2)+...

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  12. If a,b,c are positive and ar the p^(th),q^(th),r^(th) terms respective...

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  13. Prove that (x-2)(x-1) is factor of |(1,1,x),(beta+1,beta+1,beta+x),(3,...

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  14. Show that | (-a(b^2 + c^2 - a^2), 2b^3, 2c^3), (2a^3, -b(c^2 + a...

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  15. Determination the product [{:(,-4,4,4),(,-7,1,3),(,5,-3,-1):}] [{:(,1,...

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  16. If A=[1-1 1 2 1-3 1 1 1], find A^(-1) and hence solve the system of li...

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  17. Solve given system of equations by matrix method: (2)/(a)+(3)/(b)+(4...

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  18. To raise money for an orphanage, students of three schools A, B and C ...

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  19. Two cricket teams honored their players for three values, excellent ba...

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  20. If [(1,2,0),(-2,-1,-2),(0,-1,1)], find A^-1. Using A^-1, solve the sys...

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