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Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b]...

Prove that `|[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-c^3dot`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Prove that the value of each the following determinants is zero: |s...

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  2. The number of values of k for which the system of the equations (k+1)x...

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  3. Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-...

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  4. " if " |{:(a^(2),,b^(2),,c^(2)),((a+1)^(2),,(b+1)^(2),,(c+1)^(2)),((a-...

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  5. Statement 1: "Delta"= |[m y+n z, m q+n r, m b+n c],[k z-m x, k r-m ...

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  6. Prove that |[1, 1, 1]; [a, b, c]; [ bc+a^2, ac+b^2, ab+c^2]|=2(a-b)(b...

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  7. If =|sin theta cos var phi sin theta sin var phi cos theta cos theta c...

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  8. The system of equations -2x+y+z=a, x-2y+z=b, x+y-2z=c, has: (a)no so...

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  9. Show that if x1, x2, x3!=0 abs((x1+a1.b1,a1.b2,a1.b3),(a2.b1,x2+a2.b...

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  10. If determinant |[cos(theta+phi),-sin(theta+phi),cos2phi],[sin theta,co...

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  11. If Deltar =|[2^(r-1) ,2.3^(r-1), 4.5^(r-1)],[alpha,beta,gamma],[2^n-1,...

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  12. The values of k in R for which the system of equations x+k y+3z=0,k x...

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  13. A determinant of second order is made with the elements 0 and 1. Fi...

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  14. If a ,b , c are nonzero real numbers such that |[b c,c a, a b],[ c a, ...

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  15. Prove that the determinant |[x, sintheta,costheta],[-sintheta,-x,1],[...

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  16. Consider the determinant f(x)=|[0,x^2-a, x^3-b], [x^2+a,0,x^2+c], [x^4...

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  17. Find the value of |[1, 2, 4],[-1,3, 0],[4 ,1, 0]|

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  18. Consider the system of the equation k x+y+z=1,x+k y+z=k ,a n dx+y+k z=...

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  19. If x+y+z=0 prove that |[a x, b y, c z],[ c y, a z ,b x],[ b z ,c x ,a ...

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  20. Each question has four choices a, b, c and d, out of which only one is...

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