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Solve [[x+a,b,c],[a,x+b,c],[a,b,x+c]]=0...

Solve `[[x+a,b,c],[a,x+b,c],[a,b,x+c]]=0`

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

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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

ARIHANT PUBLICATION-DETERMINANTS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS (EXERCISE 5(B))
  1. Solve [[x+a,0,0],[a,x+b,0],[a,0,x+c]]=0

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  2. Solve [[a+x,a-x,a-x],[a-x,a+x,a-x],[a-x,a-x,a+x]]=0

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  3. Solve [[x+a,b,c],[a,x+b,c],[a,b,x+c]]=0

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  4. Show that x=2 is a root of [[x,-6,-1],[2,-3x,x-3],[-3,2x,x+2]]=0 S...

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  5. Evaluate [[1,a,bc],[1,b,ca],[1,c,ab]]-[[1,a,a^2],[1,b,b^2],[1,c,c^2]]

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  6. Evaluate [[a,a^2-bc,1],[b,b^2-ac,1],[c,c^2-ab,1]]

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  7. For what value of lamda the system of equations x+y+z=6, 4x+lamda y-...

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  8. If A is a 3xx3 matrix and absA=2, then which matrix is represented by ...

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  9. If A=[[0,-tan(alpha/2)],[tan(alpha/2),0]] show that (I+A) =(I-A)[[c...

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  10. If a, b and c are all positive real, then prove that minimum value of ...

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

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  12. Prove the following: [[a,b,c],[b,c,a],[c,a,b]]=3abc-a^3-b^3-c^3

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  13. Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,...

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  14. Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^...

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  15. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

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  16. Prove the following: [[b+c,a+b,a],[c+a,b+c,b],[a+b,c+a,c]] =a^3+b^...

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  17. Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =...

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  18. Prove the following: |[ax-by-cz,ay+bx,az+cx],[bx+ay,by-cz-ax,bz+cy],...

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  19. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

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  20. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

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