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a^(−1)+b^(−1)+c^(−1)=0 such that |[1+a,1...

`a^(−1)`+`b^(−1)`+`c^(−1)`=`0` such that `|[1+a,1,1,],[1,1+b,1,],[1,1,1+c,]|` =△ then the value of △ is

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Let Deltar=|[r-1,n,6],[(r-1)^2,2n^2,4n-2],[(r-1)^3,3n^3,3n^2-3n]|. Sho...

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  2. Let m be a positive integer and Deltar=|[2r-1,.^mCr,1],[m^2-1,2^m,m+1]...

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  3. a^(−1)+b^(−1)+c^(−1)=0 such that |[1+a,1,1,],[1,1+b,1,],[1,1,1+c,]| =△...

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  4. Find the area of a triangle whose vertices are A(3,2),B(11 ,8) and C(8...

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  5. If Dk=|[1, n, n];[ 2k, n^2+n+1, n^2+n];[ 2k-1, n^2, n^2+n+1]|a n...

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  6. If p+-a, q+- b, r+-c and abs((p,b,c),(a,q,c),(a,b,r)) = 0 show that p...

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  7. If x1, x2 , x3 and y1 , y2 , y3 are both in G.P. with the same common ...

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  8. If the lines a1x+b1y+1=0,a2x+b2y+1=0 and a3x+b3y+1=0 are concurrent,...

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  9. For a fixed positive integer n , if Delta=|[n !,(n+1)!,(n+2)!],[(n+1)!...

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  10. The lines 2x-y-1=0, ax+3y-3=0 and 3x+2y-2=0 are concurrent for

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  11. if f(alpha,beta)=|[cos alpha,-sin alpha,1],[sin alpha,cos alpha,1],[co...

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  12. If the lines ax+y+1=0, x+by+1=0, x+y+c=0, (a, b, c are distinct and no...

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  13. If (1+x+x^(2))^(25)=a(0)+a(1)x+a(2)x^(2)+...+a(50).x^(50), then a(0)+a...

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  14. Find the value of lambda for which the homogeneous system of equations...

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  15. If f,g,a n d \ h are differentiable functions of x and d(x)=|[f,g,h]...

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  16. Let a ,b ,c be positive and not all equal. Show that the value of the ...

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  17. if f(x)=|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)...

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  18. Without expanding a determinant at any stage, show that abs((x^2+x ,x+...

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  19. The value of determinant |[b c-a^2,a c-b^2,a b-c^2],[a c-b^2,a b-c^2,b...

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  20. Show that the system of equations 3x-y + 4z = 3, x + 2y-3z =-2 and 6x ...

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