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Without expanding, prove the following ...

Without expanding, prove the following
`|(a,b,c),(a^2,b^2,c^2),(bc,ca,ab)|=(a-b)(b-c)(c-a)(ab+bc+ca)`

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Without expanding, prove the following |(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2(a+b+c)(ab+bc+ca-a^2-b^2-c^2)

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Prove that: {:|(a^2,a,b+c),(b^2,b,c+a),(c^2,c,ab)| = -(a+b+c)(a-b)(b-c)(c-a)

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BETTER CHOICE PUBLICATION-DETERMINANTS -ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )
  1. Solve by matrix method 2x + 3y +3z = 5 x -2y + z = -4 3x - y -...

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  2. Solve by matrix method : x + 2y + z = 7, x + 3z= 11, -3y + 2x = 1.

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  3. Without expanding, prove the following |(a,b,c),(a^2,b^2,c^2),(bc,c...

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  4. Solve the following system of linear equations by matrix method : 2x -...

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  5. Solve by matrix method 3x - 2y + 3z =8 2x + y - z =1 4x -3y +2z...

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  6. Solve by matrix method 2x +y +z=1 x-2y-z =3//2 3y-5z =9

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  7. Prove that : |[y+k,y,y],[y,y+k,y],[y,y,y+k]|=k^2(3y+k).

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  8. Solve by using matrix method, 2x - 3y + 5z = 16, 3x +2y-4z=-4, x + y -...

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  9. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| =abc (1+(1)/(a)+(1)/(...

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  10. Evaluate : triangle = |[1,a,bc],[1,b,ca],[1,c,ab]|

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  11. Using determinant , find the area of triangle with verticles (1,0) ,...

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  12. Using determinants , find the area of triangle with vertices (0,0), ...

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  13. Solve the following system of linear equations by matrix method: x - y...

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  14. Solve the following system of linear equations by matrix method : 2x +...

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  15. Solve by matrix method 2/x + 3/y + 10/z = 4 , 4/x - 6/y + 5/z = 1 , ...

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  16. Show that: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

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  17. Without expanding show that following : |[a,a+b,a+b+c],[2a,3a+2b,4a+3b...

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  18. Solve the following system of linear equations by matrix method : x - ...

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  19. Solve the following equation by Matrix Method, 1/x - 1/y +2/z =7, 3/x ...

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  20. By using properties of determinants, show that : |[1,1,1],[a,b,c],[a^...

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