Home
Class 11
MATHS
If a ,\ b ,\ c are non-zero real numb...

If `a ,\ b ,\ c` are non-zero real numbers and if the system of equations `(a-1)x=y+z ,\ \ (b-1)y=z+x ,\ \ (c-1)z=x+y` has a non-trivial solution, then prove that `a b+b c+c a=a b cdot`

A

`a + b +c`

B

abc

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|92 Videos

  • CARTESIAN CO-ORDINATE SYSTEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|27 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos

Similar Questions

Explore conceptually related problems

If a , b , c are non-zero real numbers and if the system of equations (a-1)x=y+z (b-1)y=z+x (c-1)z=x+y has a non-trivial solution, then ab+bc+ca equals to (A) abc (B) a^2 - b^2 + c^2 (C) a+b -c (D) None of these

If the system of equations x=c y+b z ,\ \ y=a z+c x ,\ \ z=b x+a y has a non-trivial solution show that a^2+b^2+c^2+2a b c=1

If a, b and c are non - zero real numbers and if system of equations (a-1)x=y+z, (b-1)y=z+x and (c-1)z=x+y have a non - trivial solutin, then (3)/(2a)+(3)/(2b)+(3)/(2c) is equal to

If a , b , c are distinct real numbers and the system of equations a x+a^2y+(a^3+1)z=0 b x+b^2y+(b^3+1)z=0 c x+c^2y+(c^3+1)=0 has a non-trivial solution, show that a b c=-1

If a , b , c are distinct real numbers and the system of equations a x+a^2y+(a^3+1)z=0 b x+b^2y+(b^3+1)z=0 c x+c^2y+(c^3+1)=0 has a non-trivial solution, show that a b c=-1

If the system of equations x=c y+b z y=a z+c x z=b x+a y has a non-trivial solution, show that a^2+b^2+c^2+2a b c=1

If the system of linear equations x=cy+bz , y=az+cx , z=bx+ay has a non trivial solution show that a^2+b^2+c^2+2abc=1

The system of equations ax + 4y + z = 0,bx + 3y + z = 0, cx + 2y + z = 0 has non-trivial solution if a, b, c are in

Prove that the system of equations in xa +y+z=0 , x +by +z=0 , x +y+cz=0 has a non - trivial solution then 1/(1-a) + 1/(1-b)+ 1/(1-c)=

The system of equations -2x+y+z=a x-2y+z=b x+y-2z=c has

OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Chapter Test
  1. If x, y , z are in A.P., then the value of the det (A) is , where A ...

    Text Solution

    |

  2. The value of |(b +c,a,a),(b,c +a,b),(c,c,a +b)|, is

    Text Solution

    |

  3. If a ,\ b ,\ c are non-zero real numbers and if the system of equat...

    Text Solution

    |

  4. If a!=6,b,c satisfy|[a,2b,2c],[3,b,c],[4,a,b]|=0 ,then abc =

    Text Solution

    |

  5. The value of Delta = |(1^(2),2^(2),3^(2)),(2^(2),3^(2),4^(2)),(3^(2),4...

    Text Solution

    |

  6. Prove: |a a+b a+2b a+2b a a+b a+b a+2b a|=9(a+b)b^2

    Text Solution

    |

  7. If all the elements in a square matrix A of order 3 are equal to 1 or ...

    Text Solution

    |

  8. Sum of real roots of the euation |{:(1,4,20),(1,-2,5),(1,2x,5x^(2)):}|...

    Text Solution

    |

  9. If f(x)=|{:(sinx,cosx,tanx),(x^(3),x^(2),x),(2x,1,x):}|, then lim(xto0...

    Text Solution

    |

  10. If A, B and C are the angles of a triangle and |(1,1,1),(1 + sin A,1...

    Text Solution

    |

  11. If |(x,2,3),(2,3,x),(3,x,2)|=|(1,x,4),(x,4,1),(4,1,x)|=|(0,5,x),(5,x,0...

    Text Solution

    |

  12. Using properties of determinants, solve for x:|a+x a-x a-x a-x a+x a...

    Text Solution

    |

  13. If Delta(1) = |(7,x,2),(-5,x +1,3),(4,x,7)| and Delta(2) = |(x,2,7),(x...

    Text Solution

    |

  14. If Delta1=|{:(10,4,3),(17,7,4),(4,-5,7):}|,Delta2=|{:(4,x+5,3),(7,x+12...

    Text Solution

    |

  15. If |(a,a +d,a +2d),(a^(2),(a + d)^(2),(a + 2d)^(2)),(2a + 3d,2 (a +d),...

    Text Solution

    |

  16. If Delta(k) = |(k,1,5),(k^(2),2n +1,2n +1),(k^(3),3n^(2),3n +1)|, " th...

    Text Solution

    |

  17. If the system of equations bx + ay = c, cx + az = b, cy + bz = a h...

    Text Solution

    |

  18. If a,b,c are non-zeros, then the system of equations {:((alpha+a)x+a...

    Text Solution

    |

  19. If p^(th), q^(th),r^(th) terms an A.P are 1/a,1/b and 1/c respectively...

    Text Solution

    |

  20. If A = |(a,b,c),(x,y,z),(p,q,r)| and B = |(q,-b,y),(-p,a,-x),(r,-c,z)|...

    Text Solution

    |