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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 ENGLISH-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. a ,b ,c are distinct real numbers not equal to one. If a x+y+z=0,x+b y...

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  6. Prove that the value of the determinant |-7 5+3i2/3-4i5-3i8 4+5i2/3+4i...

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

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  8. If ar=(cos2rpi+i sin 2rpi)^(1//9) , then prove that |[a1,a2,a3],[a4,a5...

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

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  10. Using properties of determinants, prove that |(-a^2,ab,ac),(ba,-b^2,bc...

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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, b1c...

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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|=0.

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  17. A particle just clears a wall of height b at distance a and strikes...

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

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  19. If y=sinm x , then the value of the determinant |y y1y2y3y4y5y6y7y8|,w...

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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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