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Use properties of determinants ot evalua...

Use properties of determinants ot evaluate:
`{:|(x+y,y+z,z+x),(z,x,y),(1,1,1)|`

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Using properties of determinants, prove that : {:|((x+y)^2,zx,zy),(zx,(z+y)^2,xy),(zy,xy,(z+x)^2)|=2xyz(x+y+z)^3

Using properties of determinants , prove that |(x^2+1,xy,zx),(xy,y^2+1,yz),(zx,yz,z^2+1)|=1+x^2+y^2+z^2

Using the properties of determinants, show that : |[[x, y, z],[x^2, y^2, z^2],[x,y,z]]|= 0 .

Using the properties of determinants, show that : |[[x^2, y^2, z^2],[yz, zx, xy],[x,y,z]]|= (x-y)(y-z)(z-x)(xy+yz+zx) .

Using the properties of determinants, prove that : |[[a+x,y,z],[x,a+y,z],[x,y,a+z]]|=a^2(a+x+y+z)

By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+z+2x,y],[z,z,z+x+2y]| = 2(x+y+z)^3

Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]| = (1+pxyz)(x-y)(y-z)(z-x)

Using the properties of determinant, show that : |[1,x+y,x^2+y^2],[1,y+z,y^2+z^2],[1,z+x,z^2+x^2]| = (x-y)(y-z)(z-x)

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Write the value of the following determinant abs{:(a-b, b-c, c-a),(b-c...

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  2. Use properties of determinants ot evaluate: {:|(2,a,abc),(2,b,bca),(...

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  3. Use properties of determinants ot evaluate: {:|(x+y,y+z,z+x),(z,x,y)...

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  4. Evaluate |[102,18,36],[1,3,4],[17,3,6]|

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  5. Use properties of determinants ot evaluate: {:|(2,3,1),(4,6,2),(1,3,...

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  6. Use properties of determinants ot evaluate: {:|(2,3,5),(261,592,127)...

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  7. Show that x=1 is a root of the equation: {:|(x+1,2x,-11),(2x,x+1,-4...

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  8. If p,q,r ar in A.P. write the value of : {:|(x+1,x+2,x+2p),(x+2,x+3,...

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  9. Without expanding, prove that the following determinant vanishes. |...

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  10. Without actual expansion, prove that the following determinants vanish...

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  11. Without actual expansion, prove that the following determinants vanish...

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  12. Without actual expansion, prove that the following determinants vanish...

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  13. Without actual expansion, prove that the following determinants vanish...

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  14. Without actual expansion, prove that the following determinants vanish...

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  15. Without expanding, prove that Delta = abs{:(x+y, y + z, z+ x),(z, x ,...

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  16. Without expanding, prove that : |{:(1, bc, a(b+ c) ),(1, ca, b ( c+ a)...

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  17. Without expanding the determinant, show that : (frac{1}{a}+frac{1}{b}+...

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  18. (x+y+z) is fator of : {:|(x-y-z,2x,2x),(2y,y-z-x,2y),(2z,2z,z-x-y)|

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  19. Without expanding the determinant, prove that |[a,a^2,bc],[b,b^2,ca],[...

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  20. Evaluate the following: {:|(b+c,a,a),(b,c+a,b),(c,c,a+b)|

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