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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)

PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Evaluate the determinant |(1^2, 2^2, 3^2,4^2),(2^2,3^2,4^2,5^2),(3^2,4...

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  2. Without expanding, prove that |(6,2,3),(9,3,5),(12,4,7) = 0

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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 the following determinants: |(0,c,b),(c,0,a),(-b,-a,0)|

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  5. By using determinants, find the area of the triangle whose vertices ar...

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  6. By using determinants, find the area of the triangle whose vertices ar...

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  7. Find the area of the triangle whose vertices are (-2, -3), (3, 2) and ...

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  8. By using determinants, find the area of the triangle whose vertices ar...

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  9. By using determinants, find the area of the triangle whose vertices ar...

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  10. Find the value of 'x' if the area of triangle is 35 square cm. With ve...

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  11. With the help of determinants, prove that the following points are col...

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  12. With the help of determinants, prove that the following points are col...

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  13. With the help of determinants, prove that the following points are col...

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  14. Find k so that the points (3,-2), (k,2), (8,8) are collinear.

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  15. Find k if the points (2,-3), (k , 1) and (0,4) are collinear.

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  16. If the points (x,y),(a,0) and (0,b) are collinear, prove that x/a + y/...

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  17. Prove that the points (a ,\ 0),\ (0,\ b) and (1,\ 1) are collinear...

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  18. If the points (x1,y1), (x2,y2) and (x1 + x2, y1+y2) are collinear, pro...

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  19. Find p if the points (p+1,1), (2p + 1,3) and (2p + 2, 2p) are collinea...

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  20. For what value of k the points (k,2-2k),(-k+1,2k)and (-4-k,6-2k) are c...

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