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Given a=x//(y-z), b=y//(z-x), and c=z//(...

Given `a=x//(y-z), b=y//(z-x), and c=z//(x-y),w h e r e .x , y and z` are not all zero, then the value of `a b+b c+c a` is a.`0` b. `1` c.`-1""` d. none of these

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If alpha,beta,gamma are the angles of a triangle and system of equatio...

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  2. Without expanding the determinants, prove that |(103, 115, 114), (111,...

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  3. Given a=x//(y-z), b=y//(z-x), and c=z//(x-y),w h e r e .x , y and z a...

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  4. Find the value of determinant |[sqrt((13))+sqrt(3),2sqrt(5),sqrt(5)],[...

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  5. 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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  6. Prove that the value of the determinant |[-7, 5+3i,2/3-4i], [5-3i,8, 4...

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  7. If the system of linear equation x+y+z=6,x+2y+3c=14 , and 2x+5y+lambda...

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  8. If ar=(cos2rpi+i sin 2rpi)^(19) , then prove that |[a1,a2,a3],[a4,a5,a...

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  9. Let f(x)=|(2cos^2x,sin2x,-sinx),(sin2x,2sin^2x,cosx),(sinx,-cosx,0)| ....

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  10. Prove that,abs((-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2))=4a^2b^2c^2.

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  11. The number of positive integral solutions of the equation |(x^3+1,x^2y...

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  12. If the value of the determinant |(a,1, 1) (1,b,1) (1,1,c)| is positive...

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  13. By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,...

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  14. Using properties of determinants, evaluate |[18, 40 ,89],[ 40 ,89, 198...

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  15. If A1,B1,C1, are respectively, the cofactors of the elements a1, b1,c...

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  16. Solve for x |x-2 2x-3 3x-4 x-4 2x-9 3x-16 x-8 2x-27 3x-64|...

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  17. If Delta1=|[x, b, b],[ a, x, b],[ a, a, x]| a n d Delta2=|[x, b],[ a, ...

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  18. Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alp...

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  19. If y= sin px and y(n) is the nth derivative of y, then |{:(y,y(1),y(...

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  20. Find the value of the determinant |[1, 1, 1, 1],[ 1, 2, 3, 4],[ 1, 3, ...

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