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If x , y , z are have not triavle soluti...

If `x , y , z` are have not triavle solution such that `a x+y+z=0` `x+b y+z=0` `x+y+c z=0` then prove that 1/(1-a)+1/(1-b)+1/(1-c)=1

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. If the system of equations x=c y+b z ,\ \ y=a z+c x ,\ \ z=b x+a y...

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  2. If a , b , c are distinct real numbers and the system of equations a x...

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  3. If x , y , z are have not triavle solution such that a x+y+z=0 x+b y...

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  4. Solve following system of homogeneous linear equations: x+y-2z=0,\ ...

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  5. Solve following system of homogeneous linear equations: 2x+3y+4z=0,...

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  6. Solve following system of homogeneous linear equations: 3x+y+z=0,\ ...

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  7. Find the real values of lambda for which the following system of linea...

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  8. If a , b , c are non-zero real numbers and if the system of equations ...

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  9. If A is a singular matrix, then write the value of |A| .

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  10. For what value of x , the matrix [[5-x,x+1] ,[2, 4]] is singular?

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  11. Write the value of the determinant |[2, 3, 4], [5, 6, 8], [6x,9x,12x...

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  12. State whether the matrix [[2,3 ],[6, 4]] is singular or nonsingula...

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  13. Find the value of the determinant |[4200 ,4201], [4202, 4203]| .

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  14. Find the value of the determinant |[101 ,102 ,103],[ 104 ,105 ,106],...

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  15. Write the value of the determinant |[a,1,b+c], [b,1,c+a] ,[c,1,a+b]|...

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  16. If A=[[0,i],[i,1]] and B=[[0, 1],[1, 0]] , find the value of |A|+|B| .

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  17. If A=[[1, 2],[ 3,-1]] and B=[[1, 0],[-1 ,0]] , find |A B| .

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  18. Evaluate: |[4785, 4787],[ 4789, 4791]| .

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  19. If w is an imaginary cube root of unity, find the value of |[1,w, w^...

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  20. If A=[[1, 2], [3,-1]] and B=[[1,-4],[ 3,-2]] , find |A B| .

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