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Solve : |[x-a, 0, 0],[a, x-b, 0],[a, b, ...

Solve : `|[x-a, 0, 0],[a, x-b, 0],[a, b, x-c]|=0`

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The system of equations a_1x+b_1y+c_1z=0 a_2x+b_2y+c_2z=0 a_3x+b_3y+c_3z=0 [[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]]=0

Write the number of solution of the following system of equation. a_1x+b_1y+c_1z=0 a_2x+b_2y+c_2z=0 a_3x+b_3y+c_3z=0 and [[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]] =0

SHARAM PUBLICATION-DETERMINANT-EXAMPLE
  1. Without expanding prove that: |[12, 2, 4, -5, 1],[-8, 1, -5, 2, -1],[6...

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  2. Prove that: |[1, 1, 1],[a, b, c],[a^2, b^2, c^2]|=(a-b)(b-c)(c-a)

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  3. Solve : |[x-a, 0, 0],[a, x-b, 0],[a, b, x-c]|=0

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  4. What is the value of the determinant |[0, 0, 2],[0, 2, 0],[2, 0 ,0]|

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  5. Solve the following : [[1+x,1,1],[1,1+x,1],[1,1,1+x]]=0

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  6. Find the value of |{:(17,58,97),(19,60,99),(18,59,98):}| without expan...

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  7. Prove that the following. [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc(1+1/...

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  8. Evaluate the following determinants: [[0,a^2,b],[b^2,0,a^2],[a,b^2,0...

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

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  10. Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(...

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  11. Prove the following : [[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]]=0

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  12. Given the equations x=cy+bz, y=az+cx and z=bx+ay where x,y and z a...

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  13. Eliminate x,y,z from a=x/y-z, b=y/z-x, c=z/x-y

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  14. Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c]...

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  15. Prove that the following. [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc(1+1/...

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

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  17. Using properties of determinants prove that |{:(a+x,y,z),(x,a+y,z),...

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  18. Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4ab

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  19. Prove the following: [[1,1,1],[a,b,c],[a^3,b^3,c^3]] =(b-c)(c-a)(a...

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

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