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By using properties of determinants. Sho...

By using properties of determinants. Show that: (i) `|(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2` (ii) `|(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)`

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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. The number of positive integral solutions of the equation |(x^3+1,x^2y...

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

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

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

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

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

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

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

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

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

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  12. 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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  13. 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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  14. The value of |-1 2 1 3+2sqrt(2) 2+2sqrt(2) 1 3-2sqrt(2...

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

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

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  17. 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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  18. Prove that [[1+a^2+a^4, 1+a b+a^2b^2 ,1+a c+a^2c^2],[ 1+a b+a^2b^2, 1+...

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  19. The determinant |y^2-x y x^2a b c a ' b ' c '| is equal to a.|b x+a ...

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  20. If x , y , z are in A.P. , then the value of the determinant |[a+2,...

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