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Using properties of determinants, prove that `|(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2)|=4a^2 b^2 c^2`

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

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

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

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

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

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

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

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  8. If A1,B1,C1, , are respectively, the cofactors of the elements a1, b1c...

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

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

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

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

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  14. The parameter on which the value of the determinant |[1,a...

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  15. If x=c y+b z ,y=a z+c x ,z=x+a y ,w h e r e .x ,y ,z are not all zer...

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  16. If |[b^2+c^2,a b,a c],[ a b, c^2+a^2,b c],[c a, c b, a^2+b^2]|=k a^2b^...

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  17. The value of |-1 2 1 3+2sqrt(2) 2+2sqrt(2) 1 3-2sqrt(2...

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  18. Find the following system of equations is consistent, (a+1)^3x+(a+2...

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  19. Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+...

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  20. If |1 1 1a b c a^3b^2c^3|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b ,c are...

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