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Show that triangle = |[(y+z)^2,xy,zx],[x...

Show that `triangle = |[(y+z)^2,xy,zx],[xy,(x+z)^2,yz],[xz,yz,(x+y)^2]| = 2xyz(x+y+z)^3`

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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

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

Prove that: |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+zx)

Show that: |[x-y-z,2x,2x],[2y,y-z-x,2y],[2z,2z,z-x-y]|=(x+y+z)^3

Prove that |[[x,y,z],[x^2,y^2,z^2],[x^3,y^3,z^3]]|= xyz (x-y)(y-z)(z-x)

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) .

Prove that |[1,x,x^2-yz],[1,y,y^2-zx],[1,z,z^2-xy]|= 0

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)

PSEB-DETERMINANTS-Exercise
  1. Show that triangle = |[(y+z)^2,xy,zx],[xy,(x+z)^2,yz],[xz,yz,(x+y)^2]|...

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  2. Evaluate the determinant : |[2,4],[-5,-1]|

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  3. Evaluate the determinant: |[costheta,-sintheta],[sintheta,costheta]|

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  4. Evaluate the determinant : |[x^2-x+1,x+1],[x+1,x+1]|

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  5. If A = [[1,2],[4,2]], then show that |2A| = 4|A|

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  6. If A = [[1,0,1],[0,1,2],[0,0,4]] then show that |3A| = 27|A|

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  7. Evaluate the determinant : |[3,-1,-2],[0,0,-1],[3,-5,0]|

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  8. Evaluate the determinant : |[3,-4,5],[1,1,-2],[2,3,1]|

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  9. Evaluate the determinant : |[0,1,2],[-1,0,-3],[-2,3,0]|

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  10. Evaluate the determinant : |[2,-1,-2],[0,2,-1],[3,-5,0]|

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  11. If A = [[1,1,-2],[2,1,-3],[5,4,-9]], find |A|

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  12. Find values of x, if : |[2,4],[5,1]| = |[2x,4],[6,x]|

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  13. Find values of x, if : |[2,3],[4,5]| = |[x,3],[2x,5]|

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  14. If |[x,2],[18,x]| = |[6,2],[18,6]|, then x is equal to:

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  15. Using the property of determinants and without expanding , prove that:...

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  16. Using the property of determinants and without expanding , prove that:...

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  17. Using the property of determinants and without expanding , prove that:...

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  18. Using the property of determinants and without expanding , prove that:...

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  19. Using the property of determinants and without expanding , prove that:...

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  20. Using the property of determinants and without expanding , prove that:...

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  21. Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

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