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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)

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Prove that : |[x+y+z,-z,-y],[-z, x+y+z, -x],[-y,-x,x+y+z]|= 2(x+y)(y+z...

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

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  3. 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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  4. Using properties of determinants, prove that: |[3a,-a+b,-a+c],[-b+a,3b...

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  5. Solve for x":"|(a+x,a-x,a-x),(a-x,a+x,a-x),(a-x,a-x,a+x)|=0

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  6. Solve the equation |(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,3x-64)...

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  7. Prove that the determinant |[x,sintheta,costheta],[-sintheta,-x,1],[co...

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

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  9. Prove that |((b+c)^2,ab,ca),(ab,(a+c)^2,bc),(ac,bc,(a+b)^2)|=2abc(a+b...

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  10. If a, b, c are positive and unequal, show that value of the determinan...

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

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  12. Prove that: |[1,1+p,1+p+q],[2,3+2p,4+3p+2q],[3,6+3p,10+6p+3q]|=1

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  13. Prove that: |[x+y,x,x],[5x+4y,4x,2x],[10x+8y,8x,3x]|=x^3.

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  14. Prove that : {:|(a^2a^2-(b-c)^2,bc),(b^2,b^2-(c-a)^2,ca),(c^2,c^2-(a-b...

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  15. If p,q,r are not in G.P. and {:|(1,q/p,alpha+q/p),(1,r/q,alpha+r/q),...

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

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  17. Using determinants find the area of triangle with vertices (1,-1), ...

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  18. Find the area of the triangle with vertices at the points given in eac...

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  19. Find area of the triangle with vertices at the point given in the fol...

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  20. Find area of the triangle with vertices at the point given in the fol...

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