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Show that: |[a-b-c,2a,2a],[2b,b-c-a,2b],...

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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Prove: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

Prove that: |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|= 2(a+b+c)^3

Using the properties of determinants show that : |[[a^2, b^2, c^2],[bc,ca,ab],[a,b,c]]|=(a-b)(b-c)(c-a)(ab+bc+ca)

By using properties of determinants, show that : |[1,a,a^2],[1,b,b^2],[1,c,c^2]| = (a-b)(b-c)(c-a)

Using properties of determinants, show that: |[[(b+c)^2, a^2, a^2],[b^2, (c+a)^2, b^2],[c^2,c^2,(a+b)^2]]|= 2abc (a+b+c)^3 .

Using the properties of determinant, show that : |[1,a+b,a^2+b^2],[1,b+c,b^2+c^2],[1,c+a,c^2+a^2]| = (a-b)(b-c)(c-a)

Using the properties of determinants show that : |[[1, a^2+bc, a^3],[1,b^2+ac,b^3],[1,c^2+ab,c^3]]|=(a-b)(b-c)(c-a)(a^2+b^2+c^2)

Prove that : |[a+b+c,-c,-b],[-c, a+b+c, -a],[-b,-a,a+b+c]|= 2(a+b)(b+c)(c+a)

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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