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Prove that |1+a 1 1 1 1 1+b ...

Prove that `|1+a 1 1 1 1 1+b 1 1 1 1 1+c 1 1 1 1 1+d|=a b c d(a+1/a+1/b+1/c+1/d)dot` Hence find the value of the determinant if `a ,b ,c , d` are the roots of the equation `p x^4+q x^3+r x^2+s x+t=0.`

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CENGAGE-DETERMINANTS-All Questions
  1. Let "Delta"r=|r-1n6(r-1)^2 2n^2 4n-2(r-1)^2 3n^3 3n^2-3n|dot Show that...

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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. Prove that |1+a 1 1 1 1 1+b 1 1 1 1 1+c ...

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  4. Find the area of a triangle having vertices A(3,2),B(11 ,8), and C(8,1...

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  5. If Dk=1nn2k n^2+n+1n^2+n2k-1n^2n^2+n+1a n dsum(k=1)^n Dk=56. then n eq...

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  6. If a!=p ,b!=q ,c!=ra n d|p b c a q c a b r|=0, then find the value of ...

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  7. If x1,x2,x3 as well as y1, y2, y3 are in G.P. with same common rati...

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  8. If the linesa1x+b1y+1=0,\ a2x+b2y+1=0\ a n d\ a3x+b3y+1=0 are concurre...

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  9. For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)...

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  10. The number of values of a for which the lines 2x+y-1=0 , a x+3y-3=0, a...

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  11. If varphi(alpha,beta)=|cosalpha-s inalpha1s inalphacosalpha1"cos"(alph...

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  12. If the lines a x+y+1=0,x+b y+1=0a n dx+y+c=0(a ,b ,c being distinct...

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  13. If (1 + ax + b x^2)^4 = a0 +a1 x + a2 x^2 +...+a8 x^8 when a,b,a0,a1,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 dh are differentiable functions of xa n d(x)=|fgh(xf)'(xg...

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  16. If, a,b,c are positive and unequal,show that value of the determinant ...

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

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  18. Without expanding a determinant at any stage, show that ||x^2+x ,x+1 ,...

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  19. Show that |{:(bc-a^(2),,ca-b^(2),,ab-c^(2)),(ca-b^(2),,ab-c^(2),,bc-a^...

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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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